Consequences of Fluid Flow
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B A 5 m/s
5 cm
10 cm
P = 300 kPa
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B A 5 m/s
5 cm
10 cm
P = 300 kPa
CONSEQUENCES OF FLUID FLOW
CONSEQUENCES OF FLUID FLOW
The GENERAL PRINCIPLES revolving around the REYNOLDS NUMBER can be referenced on Page 105 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW
The GENERAL PRINCIPLES revolving around the REYNOLDS NUMBER can be referenced on Page 105 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B A 5 m/s
5 cm
10 cm
P = 300 kPa
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B A 5 m/s
5 cm
10 cm
P = 300 kPa
SOLUTION: REYNOLDS NUMBER: VELOCITY
vDρ vD Re = = µ υ
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B A 5 m/s
5 cm
10 cm
P = 300 kPa
SOLUTION: DENSITY OF FLUID REYNOLDS NUMBER: VELOCITY
vDρ vD Re = = µ υ
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B A 5 m/s
5 cm
10 cm
P = 300 kPa
SOLUTION: DENSITY OF FLUID REYNOLDS NUMBER: VELOCITY
vDρ vD Re = = µ υ
DIAMETER OF SECTION
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B A 5 m/s
5 cm
10 cm
P = 300 kPa
SOLUTION: DENSITY OF FLUID REYNOLDS NUMBER: VELOCITY
vDρ vD Re = = µ υ
DIAMETER OF SECTION
KINEMATIC VISCOSITY
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B A 5 m/s
5 cm
10 cm
P = 300 kPa
SOLUTION: DENSITY OF FLUID REYNOLDS NUMBER: VELOCITY
vDρ vD Re = = µ υ
DIAMETER OF SECTION
DYNAMIC VISCOSITY KINEMATIC VISCOSITY
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B
GIVEN:
A 5 m/s
5 cm
10 cm
P = 300 kPa
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: 5 cm
5 m/s
5 cm
10 cm
P = 300 kPa
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
Velocity at Point 1: 5 m/s
Diameter at Point 2: 10 cm
Kinematic Viscosity: 1.12x10-6 m2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m
5 m/s
5 cm
10 cm
P = 300 kPa
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
Velocity at Point 1: 5 m/s
Diameter at Point 2: 10 cm
Kinematic Viscosity: 1.12x10-6 m2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m
5 m/s
5 cm
10 cm
P = 300 kPa
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
Velocity at Point 1: 5 m/s
Diameter at Point 2: 10 cm
Kinematic Viscosity: 1.12x10-6 m2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m
5 m/s
5 cm
10 cm
P = 300 kPa
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
Velocity at Point 1: 5 m/s
Diameter at Point 2: 10 cm
Kinematic Viscosity: 1.12x10-6 m2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m
5 m/s
5 cm
10 cm
P = 300 kPa
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
Velocity at Point 1: 5 m/s
Diameter at Point 2: .1 m
Kinematic Viscosity: 1.12x10-6 m2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m
5 m/s
5 cm
10 cm
P = 300 kPa
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
Velocity at Point 1: 5 m/s
Diameter at Point 2: .1 m
Kinematic Viscosity: 1.12x10-6 m2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m
5 m/s
5 cm
10 cm
P = 300 kPa
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
Velocity at Point 1: 5 m/s
Diameter at Point 2: .1 m
Kinematic Viscosity: 1.12x10-6 m2/s
Velocity at Point 2: .1.26 m/s
CONTINUITY:
Q = Av
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m
5 m/s
5 cm
10 cm
Diameter at Point 2: .1 m
P = 300 kPa
Kinematic Viscosity: 1.12x10-6 m2/s
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
Velocity at Point 1: 5 m/s
Velocity at Point 2: .1.26 m/s CONTINUITY:
Q = Av
A1v1 = A2 v2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m
5 m/s
5 cm
10 cm
Diameter at Point 2: .1 m
P = 300 kPa
Kinematic Viscosity: 1.12x10-6 m2/s
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
Velocity at Point 1: 5 m/s
Velocity at Point 2: .1.26 m/s CONTINUITY:
Q = Av
A1v1 = A2 v2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m
5 m/s
5 cm
10 cm
Diameter at Point 2: .1 m
P = 300 kPa
Kinematic Viscosity: 1.12x10-6 m2/s
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
Velocity at Point 1: 5 m/s
Velocity at Point 2: .1.26 m/s CONTINUITY:
Q = Av
A1v1 = A2 v2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m
5 m/s
5 cm
10 cm
Velocity at Point 1: 5 m/s
Diameter at Point 2: .1 m
P = 300 kPa
Kinematic Viscosity: 1.12x10-6 m2/s
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
Velocity at Point 2: .1.26 m/s CONTINUITY:
Q = Av
AREA:
A1v1 = A2 v2
πd2 A= 4
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m
5 m/s
5 cm
10 cm
Velocity at Point 1: 5 m/s
Diameter at Point 2: .1 m
P = 300 kPa
Kinematic Viscosity: 1.12x10-6 m2/s
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
Velocity at Point 2: .1.26 m/s CONTINUITY:
Q = Av
AREA:
A1v1 = A2 v2
πd2 A= 4
π (.05)2 A1 = 4
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m
5 m/s
5 cm
10 cm
Velocity at Point 1: 5 m/s
Diameter at Point 2: .1 m
P = 300 kPa
Kinematic Viscosity: 1.12x10-6 m2/s
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
Velocity at Point 2: .1.26 m/s CONTINUITY:
Q = Av
AREA:
A1v1 = A2 v2
πd2 A= 4
π (.05)2 A1 = = .00198 m 2 4
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m Area at Point 1: .00198 m2
5 m/s
5 cm
10 cm
Velocity at Point 1: 5 m/s
Diameter at Point 2: .1 m
P = 300 kPa
Kinematic Viscosity: 1.12x10-6 m2/s
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
Area at Point 2: .00785 m2
Velocity at Point 2: .1.26 m/s CONTINUITY:
Q = Av
AREA:
A1v1 = A2 v2
πd2 A= 4
π (.05)2 A1 = = .00198 m 2 4
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m Area at Point 1: .00198 m2
5 m/s
5 cm
10 cm
Velocity at Point 1: 5 m/s
Diameter at Point 2: .1 m
P = 300 kPa
Kinematic Viscosity: 1.12x10-6 m2/s
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
Area at Point 2: .00785 m2
Velocity at Point 2: .1.26 m/s CONTINUITY:
Q = Av
AREA:
A1v1 = A2 v2
πd2 A= 4
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m Area at Point 1: .00198 m2
5 m/s
5 cm
10 cm
Velocity at Point 1: 5 m/s
Diameter at Point 2: .1 m
P = 300 kPa
Kinematic Viscosity: 1.12x10-6 m2/s
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
Area at Point 2: .00785 m2
Velocity at Point 2: .1.26 m/s CONTINUITY:
Q = Av
AREA:
A1v1 = A2 v2
πd2 A= 4
π (.1)2 A2 = 4
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m Area at Point 1: .00198 m2
5 m/s
5 cm
10 cm
Velocity at Point 1: 5 m/s
Diameter at Point 2: .1 m
P = 300 kPa
Kinematic Viscosity: 1.12x10-6 m2/s
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
Area at Point 2: .00785 m2
Velocity at Point 2: .1.26 m/s CONTINUITY:
Q = Av
AREA:
A1v1 = A2 v2
πd2 A= 4
π (.1)2 A2 = = .00785 m 2 4
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m Area at Point 1: .00198 m2
5 m/s
5 cm
10 cm
Velocity at Point 1: 5 m/s
Diameter at Point 2: .1 m
P = 300 kPa
Kinematic Viscosity: 1.12x10-6 m2/s
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
Area at Point 2: .00785 m2
Velocity at Point 2: .1.26 m/s CONTINUITY:
Q = Av
AREA:
A1v1 = A2 v2
πd2 A= 4
π (.1)2 A2 = = .00785 m 2 4
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m Area at Point 1: .00198 m2
5 m/s
5 cm
10 cm
Diameter at Point 2: .1 m
P = 300 kPa
vDρ vD Re = = µ υ
Area at Point 2: .00785 m2
Kinematic Viscosity: 1.12x10-6 m2/s
SOLUTION: REYNOLDS NUMBER:
Velocity at Point 1: 5 m/s
Velocity at Point 2: .1.26 m/s CONTINUITY:
Q = Av
A1v1 = A2 v2
.00198 m 2 (5 m/s) = .00785 m 2 (v2 )
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m Area at Point 1: .00198 m2
5 m/s
5 cm
10 cm
Diameter at Point 2: .1 m
P = 300 kPa
vDρ vD Re = = µ υ
Area at Point 2: .00785 m2
Kinematic Viscosity: 1.12x10-6 m2/s
SOLUTION: REYNOLDS NUMBER:
Velocity at Point 1: 5 m/s
Velocity at Point 2: .1.26 m/s CONTINUITY:
Q = Av
A1v1 = A2 v2
.00198 m 2 (5 m/s) = .00785 m 2 (v2 )
.00198 m 2 (5 m/s) v2 = .00785 m 2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m Area at Point 1: .00198 m2
5 m/s
5 cm
10 cm
Diameter at Point 2: .1 m
P = 300 kPa
vDρ vD Re = = µ υ
Area at Point 2: .00785 m2
Kinematic Viscosity: 1.12x10-6 m2/s
SOLUTION: REYNOLDS NUMBER:
Velocity at Point 1: 5 m/s
Velocity at Point 2: .1.26 m/s CONTINUITY:
Q = Av
A1v1 = A2 v2
.00198 m 2 (5 m/s) = .00785 m 2 (v2 )
.00198 m 2 (5 m/s) v2 = = 1.26 m/s 2 .00785 m
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m Area at Point 1: .00198 m2
5 m/s
5 cm
1.26 m/s
10 cm
Diameter at Point 2: .1 m
P = 300 kPa
vDρ vD Re = = µ υ
Area at Point 2: .00785 m2
Kinematic Viscosity: 1.12x10-6 m2/s
SOLUTION: REYNOLDS NUMBER:
Velocity at Point 1: 5 m/s
Velocity at Point 2: 1.26 m/s CONTINUITY:
Q = Av
A1v1 = A2 v2
.00198 m 2 (5 m/s) = .00785 m 2 (v2 )
.00198 m 2 (5 m/s) v2 = = 1.26 m/s 2 .00785 m
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m Area at Point 1: .00198 m2
5 m/s
5 cm
1.26 m/s
P = 300 kPa
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
10 cm
Velocity at Point 1: 5 m/s
Diameter at Point 2: .1 m
Area at Point 2: .00785 m2
Kinematic Viscosity: 1.12x10-6 m2/s
Velocity at Point 2: 1.26 m/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m Area at Point 1: .00198 m2
5 m/s
5 cm
1.26 m/s
P = 300 kPa
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
10 cm
Velocity at Point 1: 5 m/s
Diameter at Point 2: .1 m
Area at Point 2: .00785 m2
Kinematic Viscosity: 1.12x10-6 m2/s
Velocity at Point 2: 1.26 m/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m Area at Point 1: .00198 m2
5 m/s
5 cm
1.26 m/s
P = 300 kPa
SOLUTION: REYNOLDS NUMBER:
vDρ vD (1.26 m/s)(.1 m) Re = = = µ υ 1.12x10 -6 m 2 /s
10 cm
Velocity at Point 1: 5 m/s
Diameter at Point 2: .1 m
Area at Point 2: .00785 m2
Kinematic Viscosity: 1.12x10-6 m2/s
Velocity at Point 2: 1.26 m/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m Area at Point 1: .00198 m2
5 m/s
5 cm
1.26 m/s
P = 300 kPa
SOLUTION: REYNOLDS NUMBER:
vDρ vD (1.26 m/s)(.1 m) Re = = = = 112,500 -6 2 µ υ 1.12x10 m /s
10 cm
Velocity at Point 1: 5 m/s
Diameter at Point 2: .1 m
Area at Point 2: .00785 m2
Kinematic Viscosity: 1.12x10-6 m2/s
Velocity at Point 2: 1.26 m/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m Area at Point 1: .00198 m2
5 m/s
5 cm
1.26 m/s
10 cm
Diameter at Point 2: .1 m
P = 300 kPa
Area at Point 2: .00785 m2
Kinematic Viscosity: 1.12x10-6 m2/s
SOLUTION:
Velocity at Point 2: 1.26 m/s
REYNOLDS NUMBER:
vDρ vD (1.26 m/s)(.1 m) Re = = = = 112,500 -6 2 µ υ 1.12x10 m /s
Velocity at Point 1: 5 m/s
Re = 112,500
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number before the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m Area at Point 1: .00198 m2
5 m/s
5 cm
1.26 m/s
P = 300 kPa
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
10 cm
Velocity at Point 1: 5 m/s
Diameter at Point 2: .1 m
Area at Point 2: .00785 m2
Kinematic Viscosity: 1.12x10-6 m2/s
Velocity at Point 2: 1.26 m/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number before the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m Area at Point 1: .00198 m2
5 m/s
5 cm
1.26 m/s
P = 300 kPa
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
10 cm
Velocity at Point 1: 5 m/s
Diameter at Point 2: .1 m
Area at Point 2: .00785 m2
Kinematic Viscosity: 1.12x10-6 m2/s
Velocity at Point 2: 1.26 m/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number before the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m Area at Point 1: .00198 m2
5 m/s
5 cm
1.26 m/s
P = 300 kPa
SOLUTION: REYNOLDS NUMBER:
vDρ vD (5 m/s)(.05 m) Re = = = µ υ 1.12x10 -6 m 2 /s
10 cm
Velocity at Point 1: 5 m/s
Diameter at Point 2: .1 m
Area at Point 2: .00785 m2
Kinematic Viscosity: 1.12x10-6 m2/s
Velocity at Point 2: 1.26 m/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number before the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m Area at Point 1: .00198 m2
5 m/s
5 cm
1.26 m/s
P = 300 kPa
SOLUTION: REYNOLDS NUMBER:
vDρ vD (5 m/s)(.05 m) Re = = = = 223,214 -6 2 µ υ 1.12x10 m /s
10 cm
Velocity at Point 1: 5 m/s
Diameter at Point 2: .1 m
Area at Point 2: .00785 m2
Kinematic Viscosity: 1.12x10-6 m2/s
Velocity at Point 2: 1.26 m/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number before the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m Area at Point 1: .00198 m2
5 m/s
5 cm
1.26 m/s
10 cm
Diameter at Point 2: .1 m
P = 300 kPa
Area at Point 2: .00785 m2
Kinematic Viscosity: 1.12x10-6 m2/s
SOLUTION:
Velocity at Point 2: 1.26 m/s
REYNOLDS NUMBER:
vDρ vD (5 m/s)(.05 m) Re = = = = 223,214 -6 2 µ υ 1.12x10 m /s
Velocity at Point 1: 5 m/s
Re = 223,214
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to:
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to:
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to:
CENTERLINE
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to:
25 mm CENTERLINE
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
CONSEQUENCES OF FLUID FLOW
CONSEQUENCES OF FLUID FLOW
The GENERAL PRINCIPLES revolving around the REYNOLDS NUMBER can be referenced on Page 105 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW
The GENERAL PRINCIPLES revolving around the REYNOLDS NUMBER can be referenced on Page 105 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to:
25 mm CENTERLINE
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to:
25 mm CENTERLINE
SOLUTION: REYNOLDS NUMBER: VELOCITY
vDρ vD Re = = µ υ
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to:
25 mm CENTERLINE
SOLUTION: DENSITY OF FLUID REYNOLDS NUMBER: VELOCITY
vDρ vD Re = = µ υ
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to:
25 mm CENTERLINE
SOLUTION: DENSITY OF FLUID REYNOLDS NUMBER: VELOCITY
vDρ vD Re = = µ υ
DIAMETER OF SECTION
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to:
25 mm CENTERLINE
SOLUTION: DENSITY OF FLUID REYNOLDS NUMBER: VELOCITY
vDρ vD Re = = µ υ
DIAMETER OF SECTION
KINEMATIC VISCOSITY
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to:
25 mm CENTERLINE
SOLUTION: DENSITY OF FLUID REYNOLDS NUMBER: VELOCITY
vDρ vD Re = = µ υ
DIAMETER OF SECTION
DYNAMIC VISCOSITY KINEMATIC VISCOSITY
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to: GIVEN:
25 mm CENTERLINE
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to: GIVEN: Diameter of Pipe: 150 mm
25 mm CENTERLINE
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
Average Velocity: 3.6 m/s
Temperature of Fluid: 25oC
Kinematic Viscosity: 7.63x10-4 m2/s
Reynolds Number: 708
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to: GIVEN: Diameter of Pipe: .15 m
25 mm CENTERLINE
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
Average Velocity: 3.6 m/s
Temperature of Fluid: 25oC
Kinematic Viscosity: 7.63x10-4 m2/s
Reynolds Number: 708
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to: GIVEN: Diameter of Pipe: .15 m
25 mm CENTERLINE
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
Average Velocity: 3.6 m/s
Temperature of Fluid: 25oC
Kinematic Viscosity: 7.63x10-4 m2/s
Reynolds Number: 708
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to: GIVEN: Diameter of Pipe: .15 m
25 mm CENTERLINE
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
Average Velocity: 3.6 m/s
Temperature of Fluid: 25oC
Kinematic Viscosity: 7.63x10-4 m2/s
Reynolds Number: 708
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to: GIVEN: Diameter of Pipe: .15 m
25 mm CENTERLINE
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
Average Velocity: 3.6 m/s
Temperature of Fluid: 25oC
Kinematic Viscosity: 7.63x10-4 m2/s
Reynolds Number: 708
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to: GIVEN: Diameter of Pipe: .15 m
25 mm CENTERLINE
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
Average Velocity: 3.6 m/s
Temperature of Fluid: 25oC
Kinematic Viscosity: 7.63x10-4 m2/s
Reynolds Number: 708
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to: GIVEN: Diameter of Pipe: .15 m
25 mm CENTERLINE
SOLUTION: REYNOLDS NUMBER:
vDρ vD (3.6 m/s)(.15 m) Re = = = µ υ 7.63x10 -4 m 2 /s
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
Average Velocity: 3.6 m/s
Temperature of Fluid: 25oC
Kinematic Viscosity: 7.63x10-4 m2/s
Reynolds Number: 708
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to: GIVEN: Diameter of Pipe: .15 m
25 mm CENTERLINE
SOLUTION: REYNOLDS NUMBER:
vDρ vD (3.6 m/s)(.15 m) Re = = = = 708 -4 2 µ υ 7.63x10 m /s
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
Average Velocity: 3.6 m/s
Temperature of Fluid: 25oC
Kinematic Viscosity: 7.63x10-4 m2/s
Reynolds Number: 708
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to: GIVEN: Diameter of Pipe: .15 m
25 mm CENTERLINE
SOLUTION: REYNOLDS NUMBER:
vDρ vD (3.6 m/s)(.15 m) Re = = = = 708 -4 2 µ υ 7.63x10 m /s
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
Average Velocity: 3.6 m/s
Temperature of Fluid: 25oC
Kinematic Viscosity: 7.63x10-4 m2/s
Reynolds Number: 708
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to: GIVEN: Diameter of Pipe: .15 m
25 mm CENTERLINE
SOLUTION:
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
Average Velocity: 3.6 m/s
Temperature of Fluid: 25oC
Kinematic Viscosity: 7.63x10-4 m2/s
Reynolds Number: 708
CONSEQUENCES OF FLUID FLOW
CONSEQUENCES OF FLUID FLOW
The GENERAL PRINCIPLES revolving around VELOCITY DISTRIBUTION can be referenced on Page 105 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW
The GENERAL PRINCIPLES revolving around VELOCITY DISTRIBUTION can be referenced on Page 105 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to: GIVEN: Diameter of Pipe: .15 m
25 mm CENTERLINE
SOLUTION: VELOCITY DISTRIBUTION:
⎡ ⎛ r ⎞2⎤ v(r) = vmax ⎢1− ⎥ ⎣ ⎝ R⎠ ⎦
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
Average Velocity: 3.6 m/s
Temperature of Fluid: 25oC
Kinematic Viscosity: 7.63x10-4 m2/s
Reynolds Number: 708
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to: GIVEN: Diameter of Pipe: .15 m
25 mm CENTERLINE
SOLUTION: DISTRIBUTION: VELOCITYVELOCITY AT SPECIFIED DISTANCE
⎡ ⎛ r ⎞2⎤ v(r) = vmax ⎢1− ⎥ ⎣ ⎝ R⎠ ⎦
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
Average Velocity: 3.6 m/s
Temperature of Fluid: 25oC
Kinematic Viscosity: 7.63x10-4 m2/s
Reynolds Number: 708
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to: GIVEN: Diameter of Pipe: .15 m
25 mm CENTERLINE
SOLUTION: DISTRIBUTION: VELOCITYVELOCITY AT SPECIFIED DISTANCE
⎡ ⎛ r ⎞2⎤ v(r) = vmax ⎢1− ⎥ DISTANCE FROM CENTERLINE ⎝ ⎠ R ⎣ ⎦
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
Average Velocity: 3.6 m/s
Temperature of Fluid: 25oC
Kinematic Viscosity: 7.63x10-4 m2/s
Reynolds Number: 708
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to: GIVEN: Diameter of Pipe: .15 m
25 mm CENTERLINE
SOLUTION: DISTRIBUTION: VELOCITYVELOCITY AT SPECIFIED DISTANCE
⎡ ⎛ r ⎞2⎤ v(r) = vmax ⎢1− ⎥ DISTANCE FROM CENTERLINE ⎝ ⎠ R ⎣ ⎦
RADIUS OF PIPE
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
Average Velocity: 3.6 m/s
Temperature of Fluid: 25oC
Kinematic Viscosity: 7.63x10-4 m2/s
Reynolds Number: 708
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to: GIVEN: Diameter of Pipe: .15 m
25 mm CENTERLINE
SOLUTION: DISTRIBUTION: VELOCITYVELOCITY AT SPECIFIED DISTANCE
⎡ ⎛ r ⎞2⎤ v(r) = vmax ⎢1− ⎥ DISTANCE FROM CENTERLINE ⎝ ⎠ R ⎣ ⎦ MAXIMUM VELOCITY RADIUS OF PIPE
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
Average Velocity: 3.6 m/s
Temperature of Fluid: 25oC
Kinematic Viscosity: 7.63x10-4 m2/s
Reynolds Number: 708
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to: GIVEN: Diameter of Pipe: .15 m
25 mm CENTERLINE
SOLUTION: DISTRIBUTION: VELOCITYVELOCITY AT SPECIFIED DISTANCE
⎡ ⎛ r ⎞2⎤ v(r) = vmax ⎢1− ⎥ DISTANCE FROM CENTERLINE ⎝ ⎠ R ⎣ ⎦ MAXIMUM VELOCITY RADIUS OF PIPE
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
Average Velocity: 3.6 m/s
Temperature of Fluid: 25oC
Kinematic Viscosity: 7.63x10-4 m2/s
Reynolds Number: 708
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to: GIVEN: Diameter of Pipe: .15 m
25 mm CENTERLINE
SOLUTION: VELOCITY DISTRIBUTION:
⎡ ⎛ r ⎞2⎤ v(r) = vmax ⎢1− ⎥ ⎣ ⎝ R⎠ ⎦
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
Average Velocity: 3.6 m/s
Temperature of Fluid: 25oC
Kinematic Viscosity: 7.63x10-4 m2/s
Reynolds Number: 708
CONSEQUENCES OF FLUID FLOW
CONSEQUENCES OF FLUID FLOW
The GENERAL PRINCIPLES revolving around VELOCITY DISTRIBUTION can be referenced on Page 105 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to: GIVEN: Diameter of Pipe: .15 m
25 mm CENTERLINE
SOLUTION: VELOCITY DISTRIBUTION:
⎡ ⎛ r ⎞2⎤ v(r) = vmax ⎢1− ⎥ ⎣ ⎝ R⎠ ⎦
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
Average Velocity: 3.6 m/s
Temperature of Fluid: 25oC
Kinematic Viscosity: 7.63x10-4 m2/s
Reynolds Number: 708
MAXIMUM VELOCITY:
vmax = 2v
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to: GIVEN: Diameter of Pipe: .15 m
25 mm CENTERLINE
SOLUTION: VELOCITY DISTRIBUTION:
⎡ ⎛ r ⎞2⎤ v(r) = vmax ⎢1− ⎥ ⎣ ⎝ R⎠ ⎦
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
Average Velocity: 3.6 m/s
Temperature of Fluid: 25oC
Kinematic Viscosity: 7.63x10-4 m2/s
Reynolds Number: 708
MAXIMUM VELOCITY:
vmax = 2v = 2(3.6 m/s)
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to: GIVEN: Diameter of Pipe: .15 m
25 mm CENTERLINE
SOLUTION: VELOCITY DISTRIBUTION:
⎡ ⎛ r ⎞2⎤ v(r) = vmax ⎢1− ⎥ ⎣ ⎝ R⎠ ⎦
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
Average Velocity: 3.6 m/s
Temperature of Fluid: 25oC
Kinematic Viscosity: 7.63x10-4 m2/s
Reynolds Number: 708
MAXIMUM VELOCITY:
vmax = 2v = 2(3.6 m/s) = 7.2 m/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to: GIVEN: Diameter of Pipe: .15 m
25 mm CENTERLINE
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
Average Velocity: 3.6 m/s
Temperature of Fluid: 25oC
Kinematic Viscosity: 7.63x10-4 m2/s
SOLUTION:
Reynolds Number: 708
VELOCITY DISTRIBUTION:
Maximum Velocity: 7.2 m/s
⎡ ⎛ r ⎞2⎤ v(r) = vmax ⎢1− ⎥ ⎣ ⎝ R⎠ ⎦
MAXIMUM VELOCITY:
vmax = 2v = 2(3.6 m/s) = 7.2 m/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to: GIVEN: Diameter of Pipe: .15 m
25 mm CENTERLINE
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
Average Velocity: 3.6 m/s
Temperature of Fluid: 25oC
Kinematic Viscosity: 7.63x10-4 m2/s
SOLUTION:
Reynolds Number: 708
VELOCITY DISTRIBUTION:
Maximum Velocity: 7.2 m/s
⎡ ⎛ r ⎞2⎤ v(r) = vmax ⎢1− ⎥ ⎣ ⎝ R⎠ ⎦
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to: GIVEN: Diameter of Pipe: .15 m
25 mm CENTERLINE
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
Average Velocity: 3.6 m/s
Temperature of Fluid: 25oC
Kinematic Viscosity: 7.63x10-4 m2/s
SOLUTION:
Reynolds Number: 708
VELOCITY DISTRIBUTION:
Maximum Velocity: 7.2 m/s
⎡ ⎛ r ⎞2⎤ v(r) = vmax ⎢1− ⎥ ⎣ ⎝ R⎠ ⎦
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to: GIVEN: Diameter of Pipe: .15 m
25 mm CENTERLINE
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
Average Velocity: 3.6 m/s
Temperature of Fluid: 25oC
Kinematic Viscosity: 7.63x10-4 m2/s
SOLUTION:
Reynolds Number: 708
VELOCITY DISTRIBUTION:
Maximum Velocity: 7.2 m/s
⎡ ⎛ r ⎞2⎤ ⎡ ⎛ .25 m ⎞ 2 ⎤ v(r) = vmax ⎢1− = 7.2 m/s ⎢1− = 6.4 m/s ⎥ ⎥ ⎣ ⎝ R⎠ ⎦ ⎣ ⎝ .75 m ⎠ ⎦
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to: GIVEN: Diameter of Pipe: .15 m
25 mm CENTERLINE
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
Average Velocity: 3.6 m/s
Temperature of Fluid: 25oC
Kinematic Viscosity: 7.63x10-4 m2/s
SOLUTION:
Reynolds Number: 708
VELOCITY DISTRIBUTION:
Maximum Velocity: 7.2 m/s
⎡ ⎛ r ⎞2⎤ ⎡ ⎛ .25 m ⎞ 2 ⎤ v(r) = vmax ⎢1− = 7.2 m/s ⎢1− = 6.4 m/s ⎥ ⎥ ⎣ ⎝ R⎠ ⎦ ⎣ ⎝ .75 m ⎠ ⎦
v = 6.4 m/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: A
WATER P
FEED ELEVATION = 23 ft
DISCHARGE ELEVATION = 33 ft
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: A
WATER P
FEED ELEVATION = 23 ft
DISCHARGE ELEVATION = 33 ft
CONSEQUENCES OF FLUID FLOW
CONSEQUENCES OF FLUID FLOW
The DARCY-WEISBACH EQUATION can be referenced on Page 106 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: A
WATER P
SOLUTION: DARCY-WEISBACH EQUATION:
L v2 hf = f D 2g
FEED ELEVATION = 23 ft
DISCHARGE ELEVATION = 33 ft
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: A
WATER P
SOLUTION: DARCY-WEISBACH EQUATION: HEAD LOSS
L v2 hf = f D 2g
FEED ELEVATION = 23 ft
DISCHARGE ELEVATION = 33 ft
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: A
WATER P
SOLUTION: FRICTION FACTOR DARCY-WEISBACH EQUATION: HEAD LOSS
L v2 hf = f D 2g
FEED ELEVATION = 23 ft
DISCHARGE ELEVATION = 33 ft
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: A
WATER P
SOLUTION: FRICTION FACTOR DARCY-WEISBACH EQUATION: HEAD LOSS
L v2 hf = f D 2g
LENGTH OF PIPE RUN
FEED ELEVATION = 23 ft
DISCHARGE ELEVATION = 33 ft
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: A
WATER P
SOLUTION: FRICTION FACTOR DARCY-WEISBACH EQUATION: HEAD LOSS
L v2 hf = f D 2g
LENGTH OF PIPE RUN VELOCITY
FEED ELEVATION = 23 ft
DISCHARGE ELEVATION = 33 ft
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: A
WATER P
SOLUTION: FRICTION FACTOR DARCY-WEISBACH EQUATION: HEAD LOSS
L v2 hf = f D 2g
LENGTH OF PIPE RUN VELOCITY
LOCAL GRAVITY
FEED ELEVATION = 23 ft
DISCHARGE ELEVATION = 33 ft
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: A
WATER P
SOLUTION: FRICTION FACTOR DARCY-WEISBACH EQUATION: HEAD LOSS
L v2 hf = f D 2g DIAMETER OF PIPE LOCAL GRAVITY
LENGTH OF PIPE RUN VELOCITY
FEED ELEVATION = 23 ft
DISCHARGE ELEVATION = 33 ft
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: GIVEN: A
WATER P
SOLUTION: DARCY-WEISBACH EQUATION:
L v2 hf = f D 2g
FEED ELEVATION = 23 ft
DISCHARGE ELEVATION = 33 ft
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: GIVEN: A
WATER
DISCHARGE ELEVATION = 33 ft
Diameter of Pipe: .083 ft
Flow Rate of Fluid: 50 gpm
P
FEED ELEVATION = 23 ft
Temperature of Fluid: 60oF
Length of Pipe: 50 ft
SOLUTION:
Area of Pipe: .0054 ft2
DARCY-WEISBACH EQUATION:
Velocity in Pipe: 20.7 ft/s
L v2 hf = f D 2g
Kinematic Viscosity: 1.217x10-5 ft2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: GIVEN: A
WATER
DISCHARGE ELEVATION = 33 ft
Diameter of Pipe: .083 ft
Flow Rate of Fluid: 50 gpm
P
FEED ELEVATION = 23 ft
Temperature of Fluid: 60oF
Length of Pipe: 50 ft
SOLUTION:
Area of Pipe: .0054 ft2
DARCY-WEISBACH EQUATION:
Velocity in Pipe: 20.7 ft/s
L v2 hf = f D 2g
Kinematic Viscosity: 1.217x10-5 ft2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: GIVEN: A
DISCHARGE ELEVATION = 33 ft
WATER
Diameter of Pipe: .083 ft
Flow Rate of Fluid: 50 gpm
P
FEED ELEVATION = 23 ft
Temperature of Fluid: 60oF
Length of Pipe: 50 ft
SOLUTION: DARCY-WEISBACH EQUATION:
L v2 hf = f D 2g
Area of Pipe: .0054 ft2
CONVERSION FROM gpm TO ft3/s:
Velocity in Pipe: 20.7 ft/s
Kinematic Viscosity: 1.217x10-5 ft2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: GIVEN: A
DISCHARGE ELEVATION = 33 ft
WATER
Diameter of Pipe: .083 ft
Flow Rate of Fluid: 50 gpm
P
FEED ELEVATION = 23 ft
Temperature of Fluid: 60oF
Length of Pipe: 50 ft
SOLUTION: DARCY-WEISBACH EQUATION:
L v2 hf = f D 2g
Area of Pipe: .0054 ft2
CONVERSION FROM gpm TO ft3/s:
Gal ⎛ .134 ft 3 ⎞ ⎛ 1 min ⎞ 50 min ⎜⎝ 1 Gal ⎟⎠ ⎝ 60 s ⎠
Velocity in Pipe: 20.7 ft/s
Kinematic Viscosity: 1.217x10-5 ft2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: GIVEN: A
DISCHARGE ELEVATION = 33 ft
WATER
Diameter of Pipe: .083 ft
Flow Rate of Fluid: .112 ft3/s
P
FEED ELEVATION = 23 ft
Temperature of Fluid: 60oF
Length of Pipe: 50 ft
SOLUTION: DARCY-WEISBACH EQUATION:
L v2 hf = f D 2g
Area of Pipe: .0054 ft2
CONVERSION FROM gpm TO ft3/s:
Gal ⎛ .134 ft 3 ⎞ ⎛ 1 min ⎞ 3 50 = .112 ft /s ⎜ ⎟ min ⎝ 1 Gal ⎠ ⎝ 60 s ⎠
Velocity in Pipe: 20.7 ft/s
Kinematic Viscosity: 1.217x10-5 ft2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: GIVEN: A
WATER
DISCHARGE ELEVATION = 33 ft
Diameter of Pipe: .083 ft
Flow Rate of Fluid: .112 ft3/s
P
FEED ELEVATION = 23 ft
Temperature of Fluid: 60oF
Length of Pipe: 50 ft
SOLUTION:
Area of Pipe: .0054 ft2
DARCY-WEISBACH EQUATION:
Velocity in Pipe: 20.7 ft/s
L v2 hf = f D 2g
Kinematic Viscosity: 1.217x10-5 ft2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: GIVEN: A
WATER
DISCHARGE ELEVATION = 33 ft
Diameter of Pipe: .083 ft
Flow Rate of Fluid: .112 ft3/s
P
FEED ELEVATION = 23 ft
Temperature of Fluid: 60oF
Length of Pipe: 50 ft
SOLUTION:
Area of Pipe: .0054 ft2
DARCY-WEISBACH EQUATION:
Velocity in Pipe: 20.7 ft/s
L v2 hf = f D 2g
Kinematic Viscosity: 1.217x10-5 ft2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: GIVEN: A
WATER
DISCHARGE ELEVATION = 33 ft
Diameter of Pipe: .083 ft
Flow Rate of Fluid: .112 ft3/s
P
FEED ELEVATION = 23 ft
Temperature of Fluid: 60oF
Length of Pipe: 50 ft
SOLUTION: DARCY-WEISBACH EQUATION:
L v2 hf = f D 2g
Area of Pipe: .0054 ft2
CONTINUITY:
Velocity in Pipe: 20.7 ft/s
Kinematic Viscosity: 1.217x10-5 ft2/s
Q = Av
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: GIVEN: A
WATER
DISCHARGE ELEVATION = 33 ft
Diameter of Pipe: .083 ft
Flow Rate of Fluid: .112 ft3/s
P
FEED ELEVATION = 23 ft
Temperature of Fluid: 60oF
Length of Pipe: 50 ft
SOLUTION: DARCY-WEISBACH EQUATION:
L v2 hf = f D 2g
Area of Pipe: .0054 ft2
CONTINUITY:
Velocity in Pipe: 20.7 ft/s
Kinematic Viscosity: 1.217x10-5 ft2/s
Q = Av AREA:
πd A= 4
2
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: GIVEN: A
WATER
DISCHARGE ELEVATION = 33 ft
Diameter of Pipe: .083 ft
Flow Rate of Fluid: .112 ft3/s
P
FEED ELEVATION = 23 ft
Temperature of Fluid: 60oF
Length of Pipe: 50 ft
SOLUTION: DARCY-WEISBACH EQUATION:
L v2 hf = f D 2g
Area of Pipe: .0054 ft2
Velocity in Pipe: 20.7 ft/s
CONTINUITY:
Kinematic Viscosity: 1.217x10-5 ft2/s
Q = Av AREA:
πd A= 4
2
π (.083 ft) A= 4
2
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: GIVEN: A
DISCHARGE ELEVATION = 33 ft
WATER
Diameter of Pipe: .083 ft
Flow Rate of Fluid: .112 ft3/s
P
FEED ELEVATION = 23 ft
Temperature of Fluid: 60oF
Length of Pipe: 50 ft
SOLUTION: DARCY-WEISBACH EQUATION:
L v2 hf = f D 2g
Area of Pipe: .0054 ft2
Velocity in Pipe: 20.7 ft/s
CONTINUITY:
Kinematic Viscosity: 1.217x10-5 ft2/s
Q = Av AREA:
πd A= 4
2
π (.083 ft) 2 A= = .0054 ft 4 2
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: GIVEN: A
DISCHARGE ELEVATION = 33 ft
WATER
Diameter of Pipe: .083 ft
Flow Rate of Fluid: .112 ft3/s
P
FEED ELEVATION = 23 ft
Temperature of Fluid: 60oF
Length of Pipe: 50 ft
SOLUTION: DARCY-WEISBACH EQUATION:
L v2 hf = f D 2g
Area of Pipe: .0054 ft2
Velocity in Pipe: 20.7 ft/s
CONTINUITY:
Kinematic Viscosity: 1.217x10-5 ft2/s
Q = Av AREA:
πd A= 4
2
π (.083 ft) 2 A= = .0054 ft 4 2
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: GIVEN: A
DISCHARGE ELEVATION = 33 ft
WATER
Diameter of Pipe: .083 ft
Flow Rate of Fluid: .112 ft3/s
P
FEED ELEVATION = 23 ft
Temperature of Fluid: 60oF
Length of Pipe: 50 ft
SOLUTION: DARCY-WEISBACH EQUATION:
L v2 hf = f D 2g
Area of Pipe: .0054 ft2
Velocity in Pipe: 20.7 ft/s
CONTINUITY:
Kinematic Viscosity: 1.217x10-5 ft2/s
Q = Av
.112 ft 3 /s = (.0054 ft 2 )v
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: GIVEN: A
DISCHARGE ELEVATION = 33 ft
WATER
Diameter of Pipe: .083 ft
Flow Rate of Fluid: .112 ft3/s
FEED ELEVATION = 23 ft
P
Temperature of Fluid: 60oF
Length of Pipe: 50 ft
SOLUTION: DARCY-WEISBACH EQUATION:
L v2 hf = f D 2g
Area of Pipe: .0054 ft2
Velocity in Pipe: 20.7 ft/s
CONTINUITY:
Kinematic Viscosity: 1.217x10-5 ft2/s
Q = Av
.112 ft 3 /s = (.0054 ft 2 )v
.112 ft 3 /s v= (.0054 m 2 )
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: GIVEN: A
DISCHARGE ELEVATION = 33 ft
WATER
Diameter of Pipe: .083 ft
Flow Rate of Fluid: .112 ft3/s
P
FEED ELEVATION = 23 ft
Temperature of Fluid: 60oF
Length of Pipe: 50 ft
SOLUTION: DARCY-WEISBACH EQUATION:
L v2 hf = f D 2g
Area of Pipe: .0054 ft2
Velocity in Pipe: 20.7 ft/s
CONTINUITY:
Kinematic Viscosity: 1.217x10-5 ft2/s
Q = Av
.112 ft 3 /s = (.0054 ft 2 )v
.112 ft 3 /s v= = 20.7 ft/s 2 (.0054 m )
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: GIVEN: A
DISCHARGE ELEVATION = 33 ft
WATER
Diameter of Pipe: .083 ft
Flow Rate of Fluid: .112 ft3/s
P
FEED ELEVATION = 23 ft
Temperature of Fluid: 60oF
Length of Pipe: 50 ft
SOLUTION: DARCY-WEISBACH EQUATION:
L v2 hf = f D 2g
Area of Pipe: .0054 ft2
Velocity in Pipe: 20.7 ft/s
CONTINUITY:
Kinematic Viscosity: 1.217x10-5 ft2/s
Q = Av
.112 ft 3 /s = (.0054 ft 2 )v
.112 ft 3 /s v= = 20.7 ft/s 2 (.0054 m )
CONSEQUENCES OF FLUID FLOW
CONSEQUENCES OF FLUID FLOW
PROPERTIES OF WATER at various temperatures can be referenced on Page 114 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW
PROPERTIES OF WATER at various temperatures can be referenced on Page 114 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: GIVEN: A
WATER
DISCHARGE ELEVATION = 33 ft
Diameter of Pipe: .083 ft
Flow Rate of Fluid: .112 ft3/s
P
FEED ELEVATION = 23 ft
Temperature of Fluid: 60oF
Length of Pipe: 50 ft
SOLUTION:
Area of Pipe: .0054 ft2
DARCY-WEISBACH EQUATION:
Velocity in Pipe: 20.7 ft/s
L v2 hf = f D 2g
Kinematic Viscosity: 1.217x10-5 ft2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: GIVEN: A
WATER
DISCHARGE ELEVATION = 33 ft
Diameter of Pipe: .083 ft
Flow Rate of Fluid: .112 ft3/s
P
FEED ELEVATION = 23 ft
Temperature of Fluid: 60oF
Length of Pipe: 50 ft
SOLUTION:
Area of Pipe: .0054 ft2
DARCY-WEISBACH EQUATION:
Velocity in Pipe: 20.7 ft/s
L v2 hf = f D 2g
REYNOLDS NUMBER:
vDρ vD Re = = µ υ
Kinematic Viscosity: 1.217x10-5 ft2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: GIVEN: A
WATER
DISCHARGE ELEVATION = 33 ft
Diameter of Pipe: .083 ft
Flow Rate of Fluid: .112 ft3/s
P
FEED ELEVATION = 23 ft
Temperature of Fluid: 60oF
Length of Pipe: 50 ft
SOLUTION:
Area of Pipe: .0054 ft2
DARCY-WEISBACH EQUATION:
Velocity in Pipe: 20.7 ft/s
L v2 hf = f D 2g
REYNOLDS NUMBER:
vDρ vD Re = = µ υ
Kinematic Viscosity: 1.217x10-5 ft2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: GIVEN: A
DISCHARGE ELEVATION = 33 ft
WATER
Diameter of Pipe: .083 ft
Flow Rate of Fluid: .112 ft3/s
P
FEED ELEVATION = 23 ft
Temperature of Fluid: 60oF
Length of Pipe: 50 ft
SOLUTION:
Area of Pipe: .0054 ft2
DARCY-WEISBACH EQUATION:
Velocity in Pipe: 20.7 ft/s
L v2 hf = f D 2g
REYNOLDS NUMBER:
vDρ vD (20.7 ft/s)(.083 ft) Re = = = µ υ 1.217x10 -5 ft 2 /s
Kinematic Viscosity: 1.217x10-5 ft2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: GIVEN: A
DISCHARGE ELEVATION = 33 ft
WATER
Diameter of Pipe: .083 ft
Flow Rate of Fluid: .112 ft3/s
P
FEED ELEVATION = 23 ft
Temperature of Fluid: 60oF
Length of Pipe: 50 ft
SOLUTION:
Area of Pipe: .0054 ft2
DARCY-WEISBACH EQUATION:
Velocity in Pipe: 20.7 ft/s
L v2 hf = f D 2g
REYNOLDS NUMBER:
vDρ vD (20.7 ft/s)(.083 ft) Re = = = = 141,175 -5 2 µ υ 1.217x10 ft /s
Kinematic Viscosity: 1.217x10-5 ft2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: GIVEN: A
DISCHARGE ELEVATION = 33 ft
WATER
Diameter of Pipe: .083 ft
Flow Rate of Fluid: .112 ft3/s
P
FEED ELEVATION = 23 ft
Temperature of Fluid: 60oF
Length of Pipe: 50 ft
SOLUTION:
Area of Pipe: .0054 ft2
DARCY-WEISBACH EQUATION:
Velocity in Pipe: 20.7 ft/s
L v2 hf = f D 2g
REYNOLDS NUMBER:
vDρ vD (20.7 ft/s)(.083 ft) Re = = = = 141,175 -5 2 µ υ 1.217x10 ft /s
Kinematic Viscosity: 1.217x10-5 ft2/s
Reynolds Number: 141,175
CONSEQUENCES OF FLUID FLOW
The MOODY (STANTON) DIAGRAM can be referenced on Page 115 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW
The MOODY (STANTON) DIAGRAM can be referenced on Page 115 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW
The MOODY (STANTON) DIAGRAM can be referenced on Page 115 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW
The MOODY (STANTON) DIAGRAM can be referenced on Page 115 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW
.018 .016
The MOODY (STANTON) DIAGRAM can be referenced on Page 115 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW
.0162
The MOODY (STANTON) DIAGRAM can be referenced on Page 115 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: GIVEN: A
WATER
DISCHARGE ELEVATION = 33 ft
Diameter of Pipe: .083 ft
Flow Rate of Fluid: .112 ft3/s
P
FEED ELEVATION = 23 ft
Temperature of Fluid: 60oF
Length of Pipe: 50 ft
SOLUTION:
Area of Pipe: .0054 ft2
DARCY-WEISBACH EQUATION:
Velocity in Pipe: 20.7 ft/s
L v2 hf = f D 2g
Kinematic Viscosity: 1.217x10-5 ft2/s
Reynolds Number: 141,175
Friction Factor: .0162
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: GIVEN: A
WATER
DISCHARGE ELEVATION = 33 ft
Diameter of Pipe: .083 ft
Flow Rate of Fluid: .112 ft3/s
P
FEED ELEVATION = 23 ft
Temperature of Fluid: 60oF
Length of Pipe: 50 ft
SOLUTION:
Area of Pipe: .0054 ft2
DARCY-WEISBACH EQUATION:
Velocity in Pipe: 20.7 ft/s
L v2 hf = f D 2g
Kinematic Viscosity: 1.217x10-5 ft2/s
Reynolds Number: 141,175
Friction Factor: .0162
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: GIVEN: A
WATER
DISCHARGE ELEVATION = 33 ft
Diameter of Pipe: .083 ft
Flow Rate of Fluid: .112 ft3/s
P
FEED ELEVATION = 23 ft
Temperature of Fluid: 60oF
Length of Pipe: 50 ft
SOLUTION:
Area of Pipe: .0054 ft2
DARCY-WEISBACH EQUATION:
Velocity in Pipe: 20.7 ft/s
L v2 hf = f D 2g
Kinematic Viscosity: 1.217x10-5 ft2/s
Reynolds Number: 141,175
Friction Factor: .0162
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: GIVEN: A
WATER
DISCHARGE ELEVATION = 33 ft
Diameter of Pipe: .083 ft
Flow Rate of Fluid: .112 ft3/s
P
FEED ELEVATION = 23 ft
Temperature of Fluid: 60oF
Length of Pipe: 50 ft
SOLUTION:
Area of Pipe: .0054 ft2
DARCY-WEISBACH EQUATION:
Velocity in Pipe: 20.7 ft/s
2 ⎛ ⎞ L v2 50 ft (20.7 ft/s) ⎛ ⎞ hf = f = .0162 2 ⎟ ⎜ ⎝ ⎠ D 2g .083 ft ⎝ 2(32.2 ft/s ) ⎠
Kinematic Viscosity: 1.217x10-5 ft2/s
Reynolds Number: 141,175
Friction Factor: .0162
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: GIVEN: A
WATER
DISCHARGE ELEVATION = 33 ft
Diameter of Pipe: .083 ft
Flow Rate of Fluid: .112 ft3/s
P
FEED ELEVATION = 23 ft
Temperature of Fluid: 60oF
Length of Pipe: 50 ft
SOLUTION:
Area of Pipe: .0054 ft2
DARCY-WEISBACH EQUATION:
Velocity in Pipe: 20.7 ft/s
2 ⎛ ⎞ L v2 50 ft (20.7 ft/s) ⎛ ⎞ hf = f = .0162 = 64.9 ft 2 ⎟ ⎜ ⎝ .083 ft ⎠ ⎝ 2(32.2 ft/s ) ⎠ D 2g
Kinematic Viscosity: 1.217x10-5 ft2/s
Reynolds Number: 141,175
Friction Factor: .0162
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: GIVEN: A
DISCHARGE ELEVATION = 33 ft
WATER
Diameter of Pipe: .083 ft
Flow Rate of Fluid: .112 ft3/s
P
FEED ELEVATION = 23 ft
Temperature of Fluid: 60oF
Length of Pipe: 50 ft
SOLUTION:
Area of Pipe: .0054 ft2
DARCY-WEISBACH EQUATION:
Velocity in Pipe: 20.7 ft/s
2 ⎛ ⎞ L v2 50 ft (20.7 ft/s) ⎛ ⎞ hf = f = .0162 = 64.9 ft 2 ⎟ ⎜ ⎝ .083 ft ⎠ ⎝ 2(32.2 ft/s ) ⎠ D 2g
Kinematic Viscosity: 1.217x10-5 ft2/s
hf = 64.9 ft
Reynolds Number: 141,175
Friction Factor: .0162
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 217 ft, the head loss due to friction along the pipe run is most close to: WATER P
DISCHARGE ELEVATION = 10 ft
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: WATER P
DISCHARGE ELEVATION = 10 ft
CONSEQUENCES OF FLUID FLOW
CONSEQUENCES OF FLUID FLOW
The DARCY-WEISBACH EQUATION can be referenced on Page 106 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: WATER P
SOLUTION: DARCY-WEISBACH EQUATION:
L v2 hf = f D 2g
DISCHARGE ELEVATION = 10 ft
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: WATER P
SOLUTION: DARCY-WEISBACH EQUATION: HEAD LOSS
L v2 hf = f D 2g
DISCHARGE ELEVATION = 10 ft
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: WATER P
SOLUTION: FRICTION FACTOR DARCY-WEISBACH EQUATION: HEAD LOSS
L v2 hf = f D 2g
DISCHARGE ELEVATION = 10 ft
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: WATER P
SOLUTION: FRICTION FACTOR DARCY-WEISBACH EQUATION: HEAD LOSS
L v2 hf = f D 2g
LENGTH OF PIPE RUN
DISCHARGE ELEVATION = 10 ft
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: WATER P
SOLUTION: FRICTION FACTOR DARCY-WEISBACH EQUATION: HEAD LOSS
L v2 hf = f D 2g
LENGTH OF PIPE RUN VELOCITY
DISCHARGE ELEVATION = 10 ft
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: WATER P
SOLUTION: FRICTION FACTOR DARCY-WEISBACH EQUATION: HEAD LOSS
L v2 hf = f D 2g
LENGTH OF PIPE RUN VELOCITY
LOCAL GRAVITY
DISCHARGE ELEVATION = 10 ft
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: WATER P
SOLUTION: FRICTION FACTOR DARCY-WEISBACH EQUATION: HEAD LOSS
L v2 hf = f D 2g DIAMETER OF PIPE LOCAL GRAVITY
LENGTH OF PIPE RUN VELOCITY
DISCHARGE ELEVATION = 10 ft
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER P
SOLUTION: DARCY-WEISBACH EQUATION:
L v2 hf = f D 2g
DISCHARGE ELEVATION = 10 ft
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 3.35 ft3/s
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION:
Pipe Roughness: .0004 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .785 ft2
L v2 hf = f D 2g
Velocity in Pipe: 4.26 ft/s
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
Friction Factor: .0173
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 1500 gpm
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION:
Pipe Roughness: .0004 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .785 ft2
L v2 hf = f D 2g
Velocity in Pipe: 4.26 ft/s
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
Friction Factor: .0173
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 1500 gpm
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION: DARCY-WEISBACH EQUATION:
L v2 hf = f D 2g
Pipe Roughness: .0004 ft
CONVERSION FROM gpm TO
ft3/s:
Area of Pipe: .785 ft2
Velocity in Pipe: 4.26 ft/s
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
Friction Factor: .0173
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 1500 gpm
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION: DARCY-WEISBACH EQUATION:
L v2 hf = f D 2g
Pipe Roughness: .0004 ft
CONVERSION FROM gpm TO
Gal ⎛ .134 ft 3 ⎞ ⎛ 1 min ⎞ 1500 min ⎜⎝ 1 Gal ⎟⎠ ⎝ 60 s ⎠
ft3/s:
Area of Pipe: .785 ft2
Velocity in Pipe: 4.26 ft/s
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
Friction Factor: .0173
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 3.35 ft3/s
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION: DARCY-WEISBACH EQUATION:
L v2 hf = f D 2g
Pipe Roughness: .0004 ft
CONVERSION FROM gpm TO
ft3/s:
Gal ⎛ .134 ft 3 ⎞ ⎛ 1 min ⎞ 3 1500 = 3.35 ft /s ⎜ ⎟ min ⎝ 1 Gal ⎠ ⎝ 60 s ⎠
Area of Pipe: .785 ft2
Velocity in Pipe: 4.26 ft/s
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
Friction Factor: .0173
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 3.35 ft3/s
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION:
Pipe Roughness: .0004 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .785 ft2
L v2 hf = f D 2g
Velocity in Pipe: 4.26 ft/s
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
Friction Factor: .0173
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 3.35 ft3/s
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION:
Pipe Roughness: .0004 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .785 ft2
L v2 hf = f D 2g
Velocity in Pipe: 4.26 ft/s
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
Friction Factor: .0173
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 3.35 ft3/s
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION:
Pipe Roughness: .0004 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .785 ft2
L v2 hf = f D 2g
Velocity in Pipe: 4.26 ft/s
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
Friction Factor: .0173
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 3.35 ft3/s
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION:
Pipe Roughness: .0004 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .785 ft2
L v2 hf = f D 2g
CONTINUITY:
Velocity in Pipe: 4.26 ft/s
Q = Av
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
Friction Factor: .0173
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 3.35 ft3/s
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION:
Pipe Roughness: .0004 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .785 ft2
L v2 hf = f D 2g
CONTINUITY:
Velocity in Pipe: 4.26 ft/s
Q = Av
Reynolds Number: 402,266
AREA:
πd A= 4
Kinematic Viscosity: 1.059x10-5 ft2/s
Friction Factor: .0173
2
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 3.35 ft3/s
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION:
Pipe Roughness: .0004 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .785 ft2
L v2 hf = f D 2g
CONTINUITY:
Velocity in Pipe: 4.26 ft/s
Q = Av
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
AREA:
πd A= 4
Friction Factor: .0173
2
π (1 ft) A= 4
2
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 3.35 ft3/s
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION:
Pipe Roughness: .0004 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .785 ft2
L v2 hf = f D 2g
CONTINUITY:
Velocity in Pipe: 4.26 ft/s
Q = Av
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
AREA:
πd A= 4
Friction Factor: .0173
2
π (1 ft) 2 A= = .785 ft 4 2
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 3.35 ft3/s
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION:
Pipe Roughness: .0004 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .785 ft2
L v2 hf = f D 2g
CONTINUITY:
Velocity in Pipe: 4.26 ft/s
Q = Av
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
AREA:
πd A= 4
Friction Factor: .0173
2
π (1 ft) 2 A= = .785 ft 4 2
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 3.35 ft3/s
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION:
Pipe Roughness: .0004 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .785 ft2
L v2 hf = f D 2g
CONTINUITY:
Velocity in Pipe: 4.26 ft/s
Q = Av
3.35 ft 3 /s = (.785 ft 2 )v
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
Friction Factor: .0173
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 3.35 ft3/s
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION:
Pipe Roughness: .0004 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .785 ft2
L v2 hf = f D 2g
CONTINUITY:
Velocity in Pipe: 4.26 ft/s
Q = Av
3.35 ft 3 /s = (.785 ft 2 )v
3.35 ft 3 /s v= (.785 m 2 )
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
Friction Factor: .0173
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 3.35 ft3/s
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION:
Pipe Roughness: .0004 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .785 ft2
L v2 hf = f D 2g
CONTINUITY:
Velocity in Pipe: 4.26 ft/s
Q = Av
3.35 ft 3 /s = (.785 ft 2 )v
3.35 ft 3 /s v= = 4.26 ft/s 2 (.785 m )
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
Friction Factor: .0173
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 3.35 ft3/s
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION:
Pipe Roughness: .0004 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .785 ft2
L v2 hf = f D 2g
CONTINUITY:
Velocity in Pipe: 4.26 ft/s
Q = Av
3.35 ft 3 /s = (.785 ft 2 )v
3.35 ft 3 /s v= = 4.26 ft/s 2 (.785 m )
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
Friction Factor: .0173
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW
CONSEQUENCES OF FLUID FLOW
PROPERTIES OF WATER at various temperatures can be referenced on Page 114 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW
PROPERTIES OF WATER at various temperatures can be referenced on Page 114 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 3.35 ft3/s
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION:
Pipe Roughness: .0004 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .785 ft2
L v2 hf = f D 2g
Velocity in Pipe: 4.26 ft/s
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
Friction Factor: .0173
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 3.35 ft3/s
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION:
Pipe Roughness: .0004 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .785 ft2
L v2 hf = f D 2g
REYNOLDS NUMBER:
vDρ vD Re = = µ υ
Velocity in Pipe: 4.26 ft/s
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
Friction Factor: .0173
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 3.35 ft3/s
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION:
Pipe Roughness: .0004 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .785 ft2
L v2 hf = f D 2g
REYNOLDS NUMBER:
vDρ vD Re = = µ υ
Velocity in Pipe: 4.26 ft/s
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
Friction Factor: .0173
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 3.35 ft3/s
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION:
Pipe Roughness: .0004 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .785 ft2
L v2 hf = f D 2g
REYNOLDS NUMBER:
vDρ vD (4.26 ft/s)(1 ft) Re = = = µ υ 1.059x10 -5 ft 2 /s
Velocity in Pipe: 4.26 ft/s
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
Friction Factor: .0173
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 3.35 ft3/s
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION:
Pipe Roughness: .0004 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .785 ft2
L v2 hf = f D 2g
REYNOLDS NUMBER:
vDρ vD (4.26 ft/s)(1 ft) Re = = = = 402,266 -5 2 µ υ 1.059x10 ft /s
Velocity in Pipe: 4.26 ft/s
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
Friction Factor: .0173
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 3.35 ft3/s
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION:
Pipe Roughness: .0004 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .785 ft2
L v2 hf = f D 2g
REYNOLDS NUMBER:
vDρ vD (4.26 ft/s)(1 ft) Re = = = = 402,266 -5 2 µ υ 1.059x10 ft /s
Velocity in Pipe: 4.26 ft/s
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
Friction Factor: .0173
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW
The MOODY (STANTON) DIAGRAM can be referenced on Page 115 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW
The MOODY (STANTON) DIAGRAM can be referenced on Page 115 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 3.35 ft3/s
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION:
Pipe Roughness: .0004 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .785 ft2
L v2 hf = f D 2g
RELATIVE ROUGHNESS:
ε D
Velocity in Pipe: 4.26 ft/s
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
Friction Factor: .0173
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 3.35 ft3/s
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION:
Pipe Roughness: .0004 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .785 ft2
L v2 hf = f D 2g
RELATIVE ROUGHNESS:
ε D
Velocity in Pipe: 4.26 ft/s
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
Friction Factor: .0173
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 3.35 ft3/s
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION:
Pipe Roughness: .0004 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .785 ft2
L v2 hf = f D 2g
RELATIVE ROUGHNESS:
ε .0004 ft = D 1 ft
Velocity in Pipe: 4.26 ft/s
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
Friction Factor: .0173
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 3.35 ft3/s
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION:
Pipe Roughness: .0004 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .785 ft2
L v2 hf = f D 2g
RELATIVE ROUGHNESS:
ε .0004 ft = = .0004 D 1 ft
Velocity in Pipe: 4.26 ft/s
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
Friction Factor: .0173
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW
The MOODY (STANTON) DIAGRAM can be referenced on Page 115 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW
The MOODY (STANTON) DIAGRAM can be referenced on Page 115 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW
The MOODY (STANTON) DIAGRAM can be referenced on Page 115 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW
The MOODY (STANTON) DIAGRAM can be referenced on Page 115 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW
.018 .016
The MOODY (STANTON) DIAGRAM can be referenced on Page 115 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW
.0173
The MOODY (STANTON) DIAGRAM can be referenced on Page 115 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 3.35 ft3/s
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION:
Pipe Roughness: .0004 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .785 ft2
L v2 hf = f D 2g
Velocity in Pipe: 4.26 ft/s
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
Friction Factor: .0173
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 3.35 ft3/s
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION:
Pipe Roughness: .0004 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .785 ft2
L v2 hf = f D 2g
Velocity in Pipe: 4.26 ft/s
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
Friction Factor: .0173
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 3.35 ft3/s
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION:
Pipe Roughness: .0004 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .785 ft2
L v2 hf = f D 2g
Velocity in Pipe: 4.26 ft/s
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
Friction Factor: .0173
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 3.35 ft3/s
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION:
Pipe Roughness: .0004 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .785 ft2
2 ⎛ ⎞ L v2 507 ft (4.26 ft/s) ⎛ ⎞ hf = f = .0173 2 ⎟ ⎜ ⎝ ⎠ D 2g 1 ft ⎝ 2(32.2 ft/s ) ⎠
Velocity in Pipe: 4.26 ft/s
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
Friction Factor: .0173
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 3.35 ft3/s
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION:
Pipe Roughness: .0004 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .785 ft2
2 ⎛ ⎞ L v2 507 ft (4.26 ft/s) ⎛ ⎞ hf = f = .0173 = 2.47 ft 2 ⎟ ⎜ ⎝ 1 ft ⎠ ⎝ 2(32.2 ft/s ) ⎠ D 2g
Velocity in Pipe: 4.26 ft/s
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
Friction Factor: .0173
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 3.35 ft3/s
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION:
Pipe Roughness: .0004 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .785 ft2
2 ⎛ ⎞ L v2 507 ft (4.26 ft/s) ⎛ ⎞ hf = f = .0173 = 2.47 ft 2 ⎟ ⎜ ⎝ 1 ft ⎠ ⎝ 2(32.2 ft/s ) ⎠ D 2g
Velocity in Pipe: 4.26 ft/s
hf = 2.47 ft
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
Friction Factor: .0173
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
CONSEQUENCES OF FLUID FLOW
CONSEQUENCES OF FLUID FLOW
The DARCY-WEISBACH EQUATION can be referenced on Page 106 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW
The DARCY-WEISBACH EQUATION can be referenced on Page 106 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
SOLUTION: DARCY-WEISBACH EQUATION:
L v2 hf = f D 2g
Exit, C = 1.06
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
SOLUTION: DARCY-WEISBACH EQUATION: HEAD LOSS
L v2 hf = f D 2g
Exit, C = 1.06
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
SOLUTION: FRICTION FACTOR DARCY-WEISBACH EQUATION: HEAD LOSS
L v2 hf = f D 2g
Exit, C = 1.06
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
SOLUTION: FRICTION FACTOR DARCY-WEISBACH EQUATION: HEAD LOSS
L v2 hf = f D 2g
LENGTH OF PIPE RUN
Exit, C = 1.06
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
SOLUTION: FRICTION FACTOR DARCY-WEISBACH EQUATION: HEAD LOSS
L v2 hf = f D 2g
LENGTH OF PIPE RUN VELOCITY
Exit, C = 1.06
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
SOLUTION: FRICTION FACTOR DARCY-WEISBACH EQUATION: HEAD LOSS
L v2 hf = f D 2g
LENGTH OF PIPE RUN VELOCITY
LOCAL GRAVITY
Exit, C = 1.06
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
SOLUTION: FRICTION FACTOR DARCY-WEISBACH EQUATION: HEAD LOSS
L v2 hf = f D 2g DIAMETER OF PIPE LOCAL GRAVITY
LENGTH OF PIPE RUN VELOCITY
Exit, C = 1.06
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
SOLUTION: DARCY-WEISBACH EQUATION:
L v2 hf = f D 2g
GIVEN:
Exit, C = 1.06
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .0218 ft2
L v2 hf = f D 2g
Velocity in Pipe: 9.72 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 115,123
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: 1.6 gpm
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .0218 ft2
L v2 hf = f D 2g
Velocity in Pipe: 9.72 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 115,123
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
GIVEN:
CAST IRON (ε = .00085 ft)
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: 1.6 gpm
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION: DARCY-WEISBACH EQUATION:
L v2 hf = f D 2g
Pipe Roughness: .00085 ft
CONVERSION FROM gpm TO
ft3/s:
Area of Pipe: .0218 ft2
Velocity in Pipe: 9.72 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 115,123
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
GIVEN:
CAST IRON (ε = .00085 ft)
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: 1.6 gpm
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION: DARCY-WEISBACH EQUATION:
L v2 hf = f D 2g
Pipe Roughness: .00085 ft
CONVERSION FROM gpm TO
Gal ⎛ .134 ft 3 ⎞ ⎛ 1 min ⎞ 1.6 min ⎜⎝ 1 Gal ⎟⎠ ⎝ 60 s ⎠
ft3/s:
Area of Pipe: .0218 ft2
Velocity in Pipe: 9.72 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 115,123
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
GIVEN:
CAST IRON (ε = .00085 ft)
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION: DARCY-WEISBACH EQUATION:
L v2 hf = f D 2g
Pipe Roughness: .00085 ft
CONVERSION FROM gpm TO
ft3/s:
Gal ⎛ .134 ft 3 ⎞ ⎛ 1 min ⎞ 3 1.6 = .212 ft /s ⎜ ⎟ min ⎝ 1 Gal ⎠ ⎝ 60 s ⎠
Area of Pipe: .0218 ft2
Velocity in Pipe: 9.72 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 115,123
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .0218 ft2
L v2 hf = f D 2g
Velocity in Pipe: 9.72 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 115,123
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .0218 ft2
L v2 hf = f D 2g
Velocity in Pipe: 9.72 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 115,123
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .0218 ft2
L v2 hf = f D 2g
Velocity in Pipe: 9.72 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 115,123
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .0219 ft2
L v2 hf = f D 2g
CONTINUITY:
Velocity in Pipe: 9.72 ft/s
Q = Av
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 115,123
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .0219 ft2
L v2 hf = f D 2g
CONTINUITY:
Velocity in Pipe: 9.72 ft/s
Q = Av
Reynolds Number: 115,123
AREA:
πd A= 4
Kinematic Viscosity: 1.41x10-5 ft2/s
Friction Factor: .03
2
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .0219 ft2
L v2 hf = f D 2g
CONTINUITY:
Velocity in Pipe: 9.72 ft/s
Q = Av
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 115,123
AREA:
πd A= 4
Friction Factor: .03
2
π (.167 ft) A= 4
2
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
GIVEN:
CAST IRON (ε = .00085 ft)
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .0219 ft2
L v2 hf = f D 2g
CONTINUITY:
Velocity in Pipe: 9.72 ft/s
Q = Av
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 115,123
AREA:
πd A= 4
Friction Factor: .03
2
π (.167 ft) 2 A= = .0219 ft 4 2
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
GIVEN:
CAST IRON (ε = .00085 ft)
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .0219 ft2
L v2 hf = f D 2g
CONTINUITY:
Velocity in Pipe: 9.72 ft/s
Q = Av
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 115,123
AREA:
πd A= 4
Friction Factor: .03
2
π (.167 ft) 2 A= = .0219 ft 4 2
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
GIVEN:
CAST IRON (ε = .00085 ft)
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .0219 ft2
L v2 hf = f D 2g
CONTINUITY:
Velocity in Pipe: 9.68 ft/s
Q = Av
.212 ft 3 /s = (.0219 ft 2 )v
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 115,123
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
GIVEN:
CAST IRON (ε = .00085 ft)
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .0219 ft2
L v2 hf = f D 2g
CONTINUITY:
Velocity in Pipe: 9.68 ft/s
Q = Av
.212 ft 3 /s = (.0219 ft 2 )v
.212 ft 3 /s v= (.0219 m 2 )
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 115,123
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
GIVEN:
CAST IRON (ε = .00085 ft)
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .0219 ft2
L v2 hf = f D 2g
CONTINUITY:
Velocity in Pipe: 9.68 ft/s
Q = Av
.212 ft 3 /s = (.0219 ft 2 )v
.212 ft 3 /s v= = 9.68 ft/s 2 (.0219 m )
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 115,123
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
GIVEN:
CAST IRON (ε = .00085 ft)
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .0219 ft2
L v2 hf = f D 2g
CONTINUITY:
Velocity in Pipe: 9.68 ft/s
Q = Av
.212 ft 3 /s = (.0219 ft 2 )v
.212 ft 3 /s v= = 9.68 ft/s 2 (.0219 m )
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 115,123
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW
CONSEQUENCES OF FLUID FLOW
PROPERTIES OF WATER at various temperatures can be referenced on Page 114 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW
PROPERTIES OF WATER at various temperatures can be referenced on Page 114 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .0219 ft2
L v2 hf = f D 2g
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 115,123
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .0219 ft2
L v2 hf = f D 2g
REYNOLDS NUMBER:
vDρ vD Re = = µ υ
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .0219 ft2
L v2 hf = f D 2g
REYNOLDS NUMBER:
vDρ vD Re = = µ υ
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
GIVEN:
CAST IRON (ε = .00085 ft)
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .0219 ft2
L v2 hf = f D 2g
REYNOLDS NUMBER:
vDρ vD (9.68 ft/s)(.167 ft) Re = = = µ υ 1.41x10 -5 ft 2 /s
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .0219 ft2
L v2 hf = f D 2g
REYNOLDS NUMBER:
Velocity in Pipe: 9.68 ft/s
vDρ vD (9.68 ft/s)(.167 ft) -5 ft2/s
Re = = = = 114,650 Kinematic Viscosity: 1.41x10 µ υ 1.41x10 -5 ft 2 /s Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .0219 ft2
L v2 hf = f D 2g
REYNOLDS NUMBER:
Velocity in Pipe: 9.68 ft/s
vDρ vD (9.68 ft/s)(.167 ft) -5 ft2/s
Re = = = = 114,650 Kinematic Viscosity: 1.41x10 µ υ 1.41x10 -5 ft 2 /s Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW
The MOODY (STANTON) DIAGRAM can be referenced on Page 115 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW
The MOODY (STANTON) DIAGRAM can be referenced on Page 115 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .0219 ft2
L v2 hf = f D 2g
RELATIVE ROUGHNESS:
ε D
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .0219 ft2
L v2 hf = f D 2g
RELATIVE ROUGHNESS:
ε D
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .0219 ft2
L v2 hf = f D 2g
RELATIVE ROUGHNESS:
ε .00085 ft = D .167 ft
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .0219 ft2
L v2 hf = f D 2g
RELATIVE ROUGHNESS:
ε .00085 ft = = .005 D .167 ft
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW
The MOODY (STANTON) DIAGRAM can be referenced on Page 115 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW
The MOODY (STANTON) DIAGRAM can be referenced on Page 115 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW
The MOODY (STANTON) DIAGRAM can be referenced on Page 115 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW
The MOODY (STANTON) DIAGRAM can be referenced on Page 115 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .0219 ft2
L v2 hf = f D 2g
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .0219 ft2
L v2 hf = f D 2g
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .0219 ft2
L v2 hf = f D 2g
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .0219 ft2
2 ⎛ ⎞ L v2 290 ft (9.68 ft/s) ⎛ ⎞ hf = f = .03 2 ⎟ ⎜ ⎝ ⎠ D 2g .167 ft ⎝ 2(32.2 ft/s ) ⎠
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .0219 ft2
2 ⎛ ⎞ L v2 290 ft (9.68 ft/s) ⎛ ⎞ hf = f = .03 = 75.6 ft 2 ⎟ ⎜ ⎝ .167 ft ⎠ ⎝ 2(32.2 ft/s ) ⎠ D 2g
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION: 75.6 ft
Area of Pipe: .0219 ft2
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW
The DARCY-WEISBACH EQUATION can be referenced on Page 106 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION: 75.6 ft
Area of Pipe: .0219 ft2
Velocity in Pipe: 9.68 ft/s
MINOR LOSSES:
h f , fitting
v2 =C 2g
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION: 75.6 ft
Area of Pipe: .0219 ft2
Velocity in Pipe: 9.68 ft/s
MINOR LOSSES: HEAD LOSS
h f , fitting
v2 =C 2g
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION: 75.6 ft
Area of Pipe: .0219 ft2
LOSS COEFFICIENT MINOR LOSSES: HEAD LOSS
h f , fitting
v2 =C 2g
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION: 75.6 ft
Area of Pipe: .0219 ft2
LOSS COEFFICIENT MINOR LOSSES: HEAD LOSS VELOCITY 2 v h f , fitting = C 2g
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION: 75.6 ft
Area of Pipe: .0219 ft2
LOSS COEFFICIENT MINOR LOSSES: HEAD LOSS VELOCITY 2 v h f , fitting = C 2g LOCAL GRAVITY
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION: 75.6 ft
Area of Pipe: .0219 ft2
Velocity in Pipe: 9.68 ft/s
MINOR LOSSES:
h f , fitting
v2 =C 2g
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION: 75.6 ft
Area of Pipe: .0219 ft2
Velocity in Pipe: 9.68 ft/s
MINOR LOSSES:
h f , fitting
v2 =C 2g
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
GIVEN:
CAST IRON (ε = .00085 ft)
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION: 75.6 ft
Area of Pipe: .0219 ft2
Velocity in Pipe: 9.68 ft/s
MINOR LOSSES:
h f , fitting
Kinematic Viscosity: 1.41x10-5 ft2/s
⎛ (9.86 m/s)2 ⎞ ⎛ (9.86 m/s)2 ⎞ ⎛ (9.86 m/s)2 ⎞ v2 =C = (.5) ⎜ + (.3) ⎜ + (.3) ⎜ 2 ⎟ 2 ⎟ 2 ⎟ 2g 2(32.2 m/s ) 2(32.2 m/s ) 2(32.2 m/s )⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎛ (9.86 m/s)2 ⎞ ⎛ (9.86 m/s)2 ⎞ +(.2) ⎜ + (1.06) ⎜ 2 ⎟ ⎝ 2(32.2 m/s ) ⎠ ⎝ 2(32.2 m/s 2 ) ⎟⎠
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION: 75.6 ft
Area of Pipe: .0219 ft2
Velocity in Pipe: 9.68 ft/s
MINOR LOSSES:
h f , fitting
⎛ (9.86 m/s)2 ⎞ v2 =C = (.5 + .3 + .3 + .2 + 1.06) ⎜ 2 ⎟ 2g 2(32.2 m/s )⎠ ⎝
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION: 75.6 ft
Area of Pipe: .0219 ft2
Velocity in Pipe: 9.68 ft/s
MINOR LOSSES:
h f , fitting
⎛ (9.86 m/s)2 ⎞ v2 =C = (.5 + .3 + .3 + .2 + 1.06) ⎜ = 3.56 ft 2 ⎟ 2g ⎝ 2(32.2 m/s ) ⎠
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION: 75.6 ft
Area of Pipe: .0219 ft2
Velocity in Pipe: 9.68 ft/s
MINOR LOSSES: 3.56 ft
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION: 75.6 ft
Area of Pipe: .0219 ft2
Velocity in Pipe: 9.68 ft/s
MINOR LOSSES: 3.56 ft TOTAL HEAD LOSS: 75.6 ft + 3.56 ft
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION: 75.6 ft
Area of Pipe: .0219 ft2
Velocity in Pipe: 9.68 ft/s
MINOR LOSSES: 3.56 ft TOTAL HEAD LOSS: 75.6 ft + 3.56 ft = 79.16 ft
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
GIVEN:
CAST IRON (ε = .00085 ft)
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION: 75.6 ft
Area of Pipe: .0219 ft2
Velocity in Pipe: 9.68 ft/s
MINOR LOSSES: 3.56 ft TOTAL HEAD LOSS: 75.6 ft + 3.56 ft = 79.16 ft
Kinematic Viscosity: 1.41x10-5 ft2/s
hf,total = 79.2 ft
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW
The DARCY-WEISBACH EQUATION can be referenced on Page 106 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION: ENERGY EQUATION:
P1 (v1 )2 P2 (v2 )2 + z1 + = + z2 + + h f + h f , fitting γ 2g γ 2g
Pipe Roughness: .00085 ft
Area of Pipe: .0219 ft2
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION: PRESSURE AT POINT 1 ENERGY EQUATION:
P1 (v1 )2 P2 (v2 )2 + z1 + = + z2 + + h f + h f , fitting γ 2g γ 2g
Pipe Roughness: .00085 ft
Area of Pipe: .0219 ft2
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION: VELOCITY AT POINT 1 PRESSURE AT POINT 1 ENERGY EQUATION:
P1 (v1 )2 P2 (v2 )2 + z1 + = + z2 + + h f + h f , fitting γ 2g γ 2g
Pipe Roughness: .00085 ft
Area of Pipe: .0219 ft2
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION: VELOCITY AT POINT 1 PRESSURE AT POINT 1 ENERGY EQUATION: PRESSURE AT POINT 2
P1 (v1 )2 P2 (v2 )2 + z1 + = + z2 + + h f + h f , fitting γ 2g γ 2g
Pipe Roughness: .00085 ft
Area of Pipe: .0219 ft2
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION: VELOCITY AT POINT 1 PRESSURE AT POINT 1 ENERGY EQUATION: PRESSURE AT POINT 2 VELOCITY AT POINT 2 2 2 P1 (v1 ) P2 (v2 ) + z1 + = + z2 + + h f + h f , fitting γ 2g γ 2g
Pipe Roughness: .00085 ft
Area of Pipe: .0219 ft2
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION: VELOCITY AT POINT 1 PRESSURE AT POINT 1 ENERGY EQUATION: PRESSURE AT POINT 2 VELOCITY AT POINT 2 2 2 P1 (v1 ) P2 (v2 ) + z1 + = + z2 + + h f + h f , fitting MINOR LOSSES γ 2g γ 2g
Pipe Roughness: .00085 ft
Area of Pipe: .0219 ft2
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
VELOCITY AT POINT 1 PRESSURE AT POINT 1 ENERGY EQUATION: PRESSURE AT POINT 2 VELOCITY AT POINT 2 2 2 P1 (v1 ) P2 (v2 ) + z1 + = + z2 + + h f + h f , fitting MINOR LOSSES γ 2g γ 2g MAJOR LOSSES
Area of Pipe: .0219 ft2
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
VELOCITY AT POINT 1 PRESSURE AT POINT 1 ENERGY EQUATION: PRESSURE AT POINT 2 VELOCITY AT POINT 2 2 2 P1 (v1 ) P2 (v2 ) + z1 + = + z2 + + h f + h f , fitting MINOR LOSSES γ 2g γ 2g MAJOR LOSSES ELEVATION AT POINT 2
Area of Pipe: .0219 ft2
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
VELOCITY AT POINT 1 PRESSURE AT POINT 1 ENERGY EQUATION: PRESSURE AT POINT 2 VELOCITY AT POINT 2 2 2 P1 (v1 ) P2 (v2 ) + z1 + = + z2 + + h f + h f , fitting MINOR LOSSES γ 2g γ 2g MAJOR LOSSES ELEVATION AT POINT 2 LOCAL GRAVITY
Area of Pipe: .0219 ft2
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
VELOCITY AT POINT 1 PRESSURE AT POINT 1 ENERGY EQUATION: PRESSURE AT POINT 2 VELOCITY AT POINT 2 2 2 P1 (v1 ) P2 (v2 ) + z1 + = + z2 + + h f + h f , fitting MINOR LOSSES γ 2g γ 2g MAJOR LOSSES ELEVATION AT POINT 2
ELEVATION AT POINT 1 LOCAL GRAVITY
Area of Pipe: .0219 ft2
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
VELOCITY AT POINT 1 PRESSURE AT POINT 1 ENERGY EQUATION: PRESSURE AT POINT 2 VELOCITY AT POINT 2 2 2 P1 (v1 ) P2 (v2 ) + z1 + = + z2 + + h f + h f , fitting MINOR LOSSES γ 2g γ 2g SPECIFIC WEIGHT
MAJOR LOSSES ELEVATION AT POINT 2
ELEVATION AT POINT 1 LOCAL GRAVITY
Area of Pipe: .0219 ft2
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION: ENERGY EQUATION:
P1 (v1 )2 P2 (v2 )2 + z1 + = + z2 + + h f + h f , fitting γ 2g γ 2g
Pipe Roughness: .00085 ft
Area of Pipe: .0219 ft2
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION: ENERGY EQUATION:
P1 (v1 )2 P2 (v2 )2 + z1 + = + z2 + + h f + h f , fitting γ 2g γ 2g
Pipe Roughness: .00085 ft
Area of Pipe: .0219 ft2
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION: ENERGY EQUATION:
P1 (v1 )2 P2 (v2 )2 + z1 + = + z2 + + h f + h f , fitting γ 2g γ 2g
Pipe Roughness: .00085 ft
Area of Pipe: .0219 ft2
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION: ENERGY EQUATION:
Pipe Roughness: .00085 ft
Area of Pipe: .0219 ft2
Velocity in Pipe: 9.68 ft/s
z1 = z2 + h f + h f , fitting
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION: ENERGY EQUATION:
Pipe Roughness: .00085 ft
Area of Pipe: .0219 ft2
Velocity in Pipe: 9.68 ft/s
z1 = z2 + h f , total
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION: ENERGY EQUATION:
Pipe Roughness: .00085 ft
Area of Pipe: .0219 ft2
Velocity in Pipe: 9.68 ft/s
h f , total = z1 − z2
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION: ENERGY EQUATION:
Pipe Roughness: .00085 ft
Area of Pipe: .0219 ft2
Velocity in Pipe: 9.68 ft/s
h f , total = z1 − z2 = 92 ft − 13 ft = 79 ft
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
Area of Pipe: .0219 ft2
ENERGY EQUATION:
Velocity in Pipe: 9.68 ft/s
h f , total = z1 − z2 = 92 ft − 13 ft = 79 ft
hf,total = 79 ft
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: WATER DISCHARGE ELEVATION = 15 ft
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: WATER DISCHARGE ELEVATION = 15 ft
CONSEQUENCES OF FLUID FLOW
CONSEQUENCES OF FLUID FLOW
The driving formula for determining the PRESSURE DROP FOR LAMINAR FLOW can be referenced on Page 106 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: WATER DISCHARGE ELEVATION = 15 ft
SOLUTION: HAGEN-POISEUILLE EQUATION:
π R 4 ΔPf π D 4 ΔPf Q= = 8µL 128 µ L
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: WATER DISCHARGE ELEVATION = 15 ft
SOLUTION: HAGEN-POISEUILLE EQUATION: FLOW RATE
π R 4 ΔPf π D 4 ΔPf Q= = 8µL 128 µ L
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: WATER DISCHARGE ELEVATION = 15 ft
SOLUTION: RADIUSEQUATION: OF SECTION HAGEN-POISEUILLE FLOW RATE
π R 4 ΔPf π D 4 ΔPf Q= = 8µL 128 µ L
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: WATER DISCHARGE ELEVATION = 15 ft
SOLUTION: RADIUSEQUATION: OF SECTION HAGEN-POISEUILLE FLOW RATE DIAMETER OF SECTION 4 4 π R ΔPf π D ΔPf Q= = 8µL 128 µ L
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: WATER DISCHARGE ELEVATION = 15 ft
SOLUTION: RADIUSEQUATION: OF SECTION HAGEN-POISEUILLE FLOW RATE DIAMETER OF SECTION 4 4 π R ΔPf π D ΔPf Q= = 8µL 128 µ L PRESSURE DROP
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: WATER DISCHARGE ELEVATION = 15 ft
SOLUTION: RADIUSEQUATION: OF SECTION HAGEN-POISEUILLE FLOW RATE DIAMETER OF SECTION 4 4 π R ΔPf π D ΔPf Q= = 8µL 128 µ L PRESSURE DROP LENGTH OF PIPE
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: WATER DISCHARGE ELEVATION = 15 ft
SOLUTION: RADIUSEQUATION: OF SECTION HAGEN-POISEUILLE FLOW RATE DIAMETER OF SECTION 4 4 π R ΔPf π D ΔPf Q= = 8µL 128 µ L PRESSURE DROP DYNAMIC VISCOSITY LENGTH OF PIPE
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
SOLUTION: HAGEN-POISEUILLE EQUATION:
π R 4 ΔPf π D 4 ΔPf Q= = 8µL 128 µ L
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .12 in
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION:
Kinematic Viscosity: 1.664x10-5 ft2/s
HAGEN-POISEUILLE EQUATION:
Area of Pipe: .000079 ft2
π R 4 ΔPf π D 4 ΔPf Q= = 8µL 128 µ L
Flow Rate of Fluid: .000237 ft3/s
Absolute Dynamic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 1,802
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION:
Kinematic Viscosity: 1.664x10-5 ft2/s
HAGEN-POISEUILLE EQUATION:
Area of Pipe: .000079 ft2
π R 4 ΔPf π D 4 ΔPf Q= = 8µL 128 µ L
Flow Rate of Fluid: .000237 ft3/s
Absolute Dynamic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 1,802
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION:
Kinematic Viscosity: 1.664x10-5 ft2/s
HAGEN-POISEUILLE EQUATION:
Area of Pipe: .000079 ft2
π R 4 ΔPf π D 4 ΔPf Q= = 8µL 128 µ L
Flow Rate of Fluid: .000237 ft3/s
Absolute Dynamic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 1,802
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION:
Kinematic Viscosity: 1.664x10-5 ft2/s
HAGEN-POISEUILLE EQUATION:
Area of Pipe: .000079 ft2
π R 4 ΔPf π D 4 ΔPf Q= = 8µL 128 µ L
Flow Rate of Fluid: .000237 ft3/s
Absolute Dynamic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 1,802
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION:
Kinematic Viscosity: 1.664x10-5 ft2/s
HAGEN-POISEUILLE EQUATION:
Area of Pipe: .000079 ft2
π R 4 ΔPf π D 4 ΔPf Q= = 8µL 128 µ L
Flow Rate of Fluid: .000237 ft3/s
Absolute Dynamic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 1,802
CONSEQUENCES OF FLUID FLOW
CONSEQUENCES OF FLUID FLOW
PROPERTIES OF WATER at various temperatures can be referenced on Page 114 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW
PROPERTIES OF WATER at various temperatures can be referenced on Page 114 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION:
Kinematic Viscosity: 1.664x10-5 ft2/s
HAGEN-POISEUILLE EQUATION:
Area of Pipe: .000079 ft2
π R 4 ΔPf π D 4 ΔPf Q= = 8µL 128 µ L
Flow Rate of Fluid: .000237 ft3/s
Absolute Dynamic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 1,802
CONSEQUENCES OF FLUID FLOW
The driving formula for determining the PRESSURE DROP FOR LAMINAR FLOW can be referenced on Page 106 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION:
Kinematic Viscosity: 1.664x10-5 ft2/s
REYNOLDS NUMBER:
Area of Pipe: .000079 ft2
vDρ vD Re = = µ υ
Flow Rate of Fluid: .000237 ft3/s
Absolute Dynamic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 1,802
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION:
Kinematic Viscosity: 1.664x10-5 ft2/s
DENSITY OF FLUID REYNOLDS NUMBER: VELOCITY
vDρ vD Re = = µ υ
Area of Pipe: .000079 ft2
Flow Rate of Fluid: .000237 ft3/s
DIAMETER OF SECTION
DYNAMIC VISCOSITY KINEMATIC VISCOSITY
Absolute Dynamic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 1,802
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION:
Kinematic Viscosity: 1.664x10-5 ft2/s
DENSITY OF FLUID REYNOLDS NUMBER: VELOCITY
vDρ vD Re = = µ υ
Area of Pipe: .000079 ft2
Flow Rate of Fluid: .000237 ft3/s
DIAMETER OF SECTION
DYNAMIC VISCOSITY KINEMATIC VISCOSITY
Absolute Dynamic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 1,802
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION:
Kinematic Viscosity: 1.664x10-5 ft2/s
REYNOLDS NUMBER:
Area of Pipe: .000079 ft2
vDρ vD Re = = µ υ
Flow Rate of Fluid: .000237 ft3/s
Absolute Dynamic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 1,802
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION:
Kinematic Viscosity: 1.664x10-5 ft2/s
REYNOLDS NUMBER:
Reynolds Number: 1,802
vDρ vD (3 ft/s)(.01 ft) Re = = = µ υ 1.664x10 −5 ft 2 /s
Area of Pipe: .000079 ft2
Flow Rate of Fluid: .000237 ft3/s
Absolute Dynamic Viscosity: 1.41x10-5 ft2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION:
Kinematic Viscosity: 1.664x10-5 ft2/s
REYNOLDS NUMBER:
Reynolds Number: 1,802
vDρ vD (3 ft/s)(.01 ft) Re = = = = 1,802 −5 2 µ υ 1.664x10 ft /s
Area of Pipe: .000079 ft2
Flow Rate of Fluid: .000237 ft3/s
Absolute Dynamic Viscosity: 1.41x10-5 ft2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION:
Kinematic Viscosity: 1.664x10-5 ft2/s
REYNOLDS NUMBER:
Reynolds Number: 1,802
vDρ vD (3 ft/s)(.01 ft) Re = = = = 1,802 −5 2 µ υ 1.664x10 ft /s
Area of Pipe: .000079 ft2
Flow Rate of Fluid: .000237 ft3/s
Absolute Dynamic Viscosity: 1.41x10-5 ft2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION:
Kinematic Viscosity: 1.664x10-5 ft2/s
REYNOLDS NUMBER:
Reynolds Number: 1,802 (LAMINAR FLOW)
vDρ vD (3 ft/s)(.01 ft) Re = = = = 1,802 −5 2 µ υ 1.664x10 ft /s
Area of Pipe: .000079 ft2
Flow Rate of Fluid: .000237 ft3/s
Absolute Dynamic Viscosity: 1.41x10-5 ft2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION:
Kinematic Viscosity: 1.664x10-5 ft2/s
HAGEN-POISEUILLE EQUATION:
Reynolds Number: 1,802 (LAMINAR FLOW)
π R 4 ΔPf π D 4 ΔPf Q= = 8µL 128 µ L
Area of Pipe: .000079 ft2
Flow Rate of Fluid: .000237 ft3/s
Absolute Dynamic Viscosity: 1.41x10-5 ft2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION: HAGEN-POISEUILLE EQUATION:
π R 4 ΔPf π D 4 ΔPf Q= = 8µL 128 µ L
Kinematic Viscosity: 1.664x10-5 ft2/s
FLOW RATE:
Reynolds Number: 1,802 (LAMINAR FLOW)
Area of Pipe: .000079 ft2
Q = Av
Flow Rate of Fluid: .000237 ft3/s
Absolute Dynamic Viscosity: 1.41x10-5 ft2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION: HAGEN-POISEUILLE EQUATION:
π R 4 ΔPf π D 4 ΔPf Q= = 8µL 128 µ L
Kinematic Viscosity: 1.664x10-5 ft2/s
FLOW RATE:
Reynolds Number: 1,802 (LAMINAR FLOW)
Area of Pipe: .000079 ft2
Q = Av AREA:
πd2 A= 4
Flow Rate of Fluid: .000237 ft3/s
Absolute Dynamic Viscosity: 1.41x10-5 ft2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION: HAGEN-POISEUILLE EQUATION:
π R 4 ΔPf π D 4 ΔPf Q= = 8µL 128 µ L
Kinematic Viscosity: 1.664x10-5 ft2/s
Reynolds Number: 1,802 (LAMINAR FLOW)
FLOW RATE:
Area of Pipe: .000079 ft2
Q = Av
Flow Rate of Fluid: .000237 ft3/s
Absolute Dynamic Viscosity: 1.41x10-5 ft2/s
AREA:
πd2 A= 4
π (.01 ft)2 A= 4
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION: HAGEN-POISEUILLE EQUATION:
π R 4 ΔPf π D 4 ΔPf Q= = 8µL 128 µ L
Kinematic Viscosity: 1.664x10-5 ft2/s
Reynolds Number: 1,802 (LAMINAR FLOW)
FLOW RATE:
Area of Pipe: .000079 ft2
Q = Av
Flow Rate of Fluid: .000237 ft3/s
Absolute Dynamic Viscosity: 1.41x10-5 ft2/s
AREA:
πd2 A= 4
π (.01 ft)2 2 A= = .000079 ft 4
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION: HAGEN-POISEUILLE EQUATION:
π R 4 ΔPf π D 4 ΔPf Q= = 8µL 128 µ L
Kinematic Viscosity: 1.664x10-5 ft2/s
Reynolds Number: 1,802 (LAMINAR FLOW)
FLOW RATE:
Area of Pipe: .000079 ft2
Q = Av
Flow Rate of Fluid: .000237 ft3/s
Absolute Dynamic Viscosity: 1.41x10-5 ft2/s
AREA:
πd2 A= 4
π (.01 ft)2 2 A= = .000079 ft 4
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION: HAGEN-POISEUILLE EQUATION:
π R 4 ΔPf π D 4 ΔPf Q= = 8µL 128 µ L
Kinematic Viscosity: 1.664x10-5 ft2/s
Reynolds Number: 1,802 (LAMINAR FLOW)
FLOW RATE:
Area of Pipe: .000079 ft2
Q = Av
Flow Rate of Fluid: .000237 ft3/s
Q = (.000079 ft )(3 ft/s) 2
Absolute Dynamic Viscosity: 1.41x10-5 ft2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION: HAGEN-POISEUILLE EQUATION:
π R 4 ΔPf π D 4 ΔPf Q= = 8µL 128 µ L
Kinematic Viscosity: 1.664x10-5 ft2/s
Reynolds Number: 1,802 (LAMINAR FLOW)
FLOW RATE:
Area of Pipe: .000079 ft2
Q = Av
Flow Rate of Fluid: .000237 ft3/s
Q = (.000079 ft )(3 ft/s) = .000237 ft /s 2
3
Absolute Dynamic Viscosity: 1.41x10-5 ft2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION: HAGEN-POISEUILLE EQUATION:
π R 4 ΔPf π D 4 ΔPf Q= = 8µL 128 µ L
Kinematic Viscosity: 1.664x10-5 ft2/s
Reynolds Number: 1,802 (LAMINAR FLOW)
FLOW RATE:
Area of Pipe: .000079 ft2
Q = Av
Flow Rate of Fluid: .000237 ft3/s
Q = (.000079 ft )(3 ft/s) = .000237 ft /s 2
3
Absolute Dynamic Viscosity: 1.41x10-5 ft2/s
CONSEQUENCES OF FLUID FLOW
CONSEQUENCES OF FLUID FLOW
PROPERTIES OF WATER at various temperatures can be referenced on Page 114 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW
PROPERTIES OF WATER at various temperatures can be referenced on Page 114 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION:
Kinematic Viscosity: 1.664x10-5 ft2/s
HAGEN-POISEUILLE EQUATION:
Reynolds Number: 1,802 (LAMINAR FLOW)
π R 4 ΔPf π D 4 ΔPf Q= = 8µL 128 µ L
Area of Pipe: .000079 ft2
Flow Rate of Fluid: .000237 ft3/s
Dynamic Viscosity: 3.229x10-5 lbf·s/ft2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION:
Kinematic Viscosity: 1.664x10-5 ft2/s
HAGEN-POISEUILLE EQUATION:
Reynolds Number: 1,802 (LAMINAR FLOW)
π R 4 ΔPf π D 4 ΔPf Q= = 8µL 128 µ L
Area of Pipe: .000079 ft2
Flow Rate of Fluid: .000237 ft3/s
Dynamic Viscosity: 3.229x10-5 lbf·s/ft2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION:
Kinematic Viscosity: 1.664x10-5 ft2/s
HAGEN-POISEUILLE EQUATION:
Reynolds Number: 1,802 (LAMINAR FLOW)
π R 4 ΔPf π D 4 ΔPf Q= = 8µL 128 µ L
Area of Pipe: .000079 ft2
Flow Rate of Fluid: .000237 ft3/s
Dynamic Viscosity: 3.229x10-5 lbf·s/ft2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION:
Kinematic Viscosity: 1.664x10-5 ft2/s
HAGEN-POISEUILLE EQUATION:
Reynolds Number: 1,802 (LAMINAR FLOW)
π D 4 ΔPf Q= 128 µ L
Area of Pipe: .000079 ft2
Flow Rate of Fluid: .000237 ft3/s
Dynamic Viscosity: 3.229x10-5 lbf·s/ft2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION:
Kinematic Viscosity: 1.664x10-5 ft2/s
HAGEN-POISEUILLE EQUATION:
Reynolds Number: 1,802 (LAMINAR FLOW)
4 π (.01 ft) ΔPf 3 .000237 ft /s = -5 2 128(3.229x10 lbf/ft )(30 ft)
Area of Pipe: .000079 ft2
Flow Rate of Fluid: .000237 ft3/s
Dynamic Viscosity: 3.229x10-5 lbf·s/ft2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION:
Kinematic Viscosity: 1.664x10-5 ft2/s
HAGEN-POISEUILLE EQUATION:
Reynolds Number: 1,802 (LAMINAR FLOW)
.000237 ft 3 /s ⎡⎣128(3.229x10 -5 lbf/ft 2 )(30 ft) ⎤⎦ ΔPf = 4 π (.01 ft)
Area of Pipe: .000079 ft2
Flow Rate of Fluid: .000237 ft3/s
Dynamic Viscosity: 3.229x10-5 lbf·s/ft2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION:
Kinematic Viscosity: 1.664x10-5 ft2/s
HAGEN-POISEUILLE EQUATION:
Reynolds Number: 1,802 (LAMINAR FLOW)
.000237 ft 3 /s ⎡⎣128(3.229x10 -5 lbf/ft 2 )(30 ft) ⎤⎦ 2 ΔPf = = 935 lbf/ft 4 π (.01 ft)
Area of Pipe: .000079 ft2
Flow Rate of Fluid: .000237 ft3/s
Dynamic Viscosity: 3.229x10-5 lbf·s/ft2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION:
Kinematic Viscosity: 1.664x10-5 ft2/s
HAGEN-POISEUILLE EQUATION:
Reynolds Number: 1,802 (LAMINAR FLOW)
ΔPf = 935 lbf/ft
2
Area of Pipe: .000079 ft2
Flow Rate of Fluid: .000237 ft3/s
Dynamic Viscosity: 3.229x10-5 lbf·s/ft2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION:
Kinematic Viscosity: 1.664x10-5 ft2/s
HAGEN-POISEUILLE EQUATION:
ΔPf = 935 lbf/ft
2
CONVERSION FROM lbf/ft2 TO lbf/in2:
Reynolds Number: 1,802 (LAMINAR FLOW)
Area of Pipe: .000079 ft2
Flow Rate of Fluid: .000237 ft3/s
Dynamic Viscosity: 3.229x10-5 lbf·s/ft2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION:
Kinematic Viscosity: 1.664x10-5 ft2/s
HAGEN-POISEUILLE EQUATION:
ΔPf = 935 lbf/ft
2
CONVERSION FROM lbf/ft2 TO lbf/in2:
lbf ⎛ 1 ft 2 ⎞ 935 2 ⎜ 2⎟ ft ⎝ 144 in ⎠
Reynolds Number: 1,802 (LAMINAR FLOW)
Area of Pipe: .000079 ft2
Flow Rate of Fluid: .000237 ft3/s
Dynamic Viscosity: 3.229x10-5 lbf·s/ft2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION:
Kinematic Viscosity: 1.664x10-5 ft2/s
HAGEN-POISEUILLE EQUATION:
ΔPf = 935 lbf/ft
2
CONVERSION FROM lbf/ft2 TO lbf/in2:
lbf ⎛ 1 ft 2 ⎞ 2 935 2 ⎜ = 6.49 lbf/in 2⎟ ft ⎝ 144 in ⎠
Reynolds Number: 1,802 (LAMINAR FLOW)
Area of Pipe: .000079 ft2
Flow Rate of Fluid: .000237 ft3/s
Dynamic Viscosity: 3.229x10-5 lbf·s/ft2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION:
Kinematic Viscosity: 1.664x10-5 ft2/s
HAGEN-POISEUILLE EQUATION:
ΔPf = 935 lbf/ft
2
CONVERSION FROM lbf/ft2 TO lbf/in2:
lbf ⎛ 1 ft 2 ⎞ 2 935 2 ⎜ = 6.49 lbf/in 2⎟ ft ⎝ 144 in ⎠
ΔPf = 6.49 psi
Reynolds Number: 1,802 (LAMINAR FLOW)
Area of Pipe: .000079 ft2
Flow Rate of Fluid: .000237 ft3/s
Dynamic Viscosity: 3.229x10-5 lbf·s/ft2
B A 5 m/s
5 cm
10 cm
P = 300 kPa
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B A 5 m/s
5 cm
10 cm
P = 300 kPa
CONSEQUENCES OF FLUID FLOW
CONSEQUENCES OF FLUID FLOW
The GENERAL PRINCIPLES revolving around the REYNOLDS NUMBER can be referenced on Page 105 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW
The GENERAL PRINCIPLES revolving around the REYNOLDS NUMBER can be referenced on Page 105 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B A 5 m/s
5 cm
10 cm
P = 300 kPa
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B A 5 m/s
5 cm
10 cm
P = 300 kPa
SOLUTION: REYNOLDS NUMBER: VELOCITY
vDρ vD Re = = µ υ
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B A 5 m/s
5 cm
10 cm
P = 300 kPa
SOLUTION: DENSITY OF FLUID REYNOLDS NUMBER: VELOCITY
vDρ vD Re = = µ υ
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B A 5 m/s
5 cm
10 cm
P = 300 kPa
SOLUTION: DENSITY OF FLUID REYNOLDS NUMBER: VELOCITY
vDρ vD Re = = µ υ
DIAMETER OF SECTION
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B A 5 m/s
5 cm
10 cm
P = 300 kPa
SOLUTION: DENSITY OF FLUID REYNOLDS NUMBER: VELOCITY
vDρ vD Re = = µ υ
DIAMETER OF SECTION
KINEMATIC VISCOSITY
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B A 5 m/s
5 cm
10 cm
P = 300 kPa
SOLUTION: DENSITY OF FLUID REYNOLDS NUMBER: VELOCITY
vDρ vD Re = = µ υ
DIAMETER OF SECTION
DYNAMIC VISCOSITY KINEMATIC VISCOSITY
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B
GIVEN:
A 5 m/s
5 cm
10 cm
P = 300 kPa
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: 5 cm
5 m/s
5 cm
10 cm
P = 300 kPa
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
Velocity at Point 1: 5 m/s
Diameter at Point 2: 10 cm
Kinematic Viscosity: 1.12x10-6 m2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m
5 m/s
5 cm
10 cm
P = 300 kPa
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
Velocity at Point 1: 5 m/s
Diameter at Point 2: 10 cm
Kinematic Viscosity: 1.12x10-6 m2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m
5 m/s
5 cm
10 cm
P = 300 kPa
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
Velocity at Point 1: 5 m/s
Diameter at Point 2: 10 cm
Kinematic Viscosity: 1.12x10-6 m2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m
5 m/s
5 cm
10 cm
P = 300 kPa
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
Velocity at Point 1: 5 m/s
Diameter at Point 2: 10 cm
Kinematic Viscosity: 1.12x10-6 m2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m
5 m/s
5 cm
10 cm
P = 300 kPa
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
Velocity at Point 1: 5 m/s
Diameter at Point 2: .1 m
Kinematic Viscosity: 1.12x10-6 m2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m
5 m/s
5 cm
10 cm
P = 300 kPa
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
Velocity at Point 1: 5 m/s
Diameter at Point 2: .1 m
Kinematic Viscosity: 1.12x10-6 m2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m
5 m/s
5 cm
10 cm
P = 300 kPa
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
Velocity at Point 1: 5 m/s
Diameter at Point 2: .1 m
Kinematic Viscosity: 1.12x10-6 m2/s
Velocity at Point 2: .1.26 m/s
CONTINUITY:
Q = Av
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m
5 m/s
5 cm
10 cm
Diameter at Point 2: .1 m
P = 300 kPa
Kinematic Viscosity: 1.12x10-6 m2/s
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
Velocity at Point 1: 5 m/s
Velocity at Point 2: .1.26 m/s CONTINUITY:
Q = Av
A1v1 = A2 v2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m
5 m/s
5 cm
10 cm
Diameter at Point 2: .1 m
P = 300 kPa
Kinematic Viscosity: 1.12x10-6 m2/s
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
Velocity at Point 1: 5 m/s
Velocity at Point 2: .1.26 m/s CONTINUITY:
Q = Av
A1v1 = A2 v2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m
5 m/s
5 cm
10 cm
Diameter at Point 2: .1 m
P = 300 kPa
Kinematic Viscosity: 1.12x10-6 m2/s
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
Velocity at Point 1: 5 m/s
Velocity at Point 2: .1.26 m/s CONTINUITY:
Q = Av
A1v1 = A2 v2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m
5 m/s
5 cm
10 cm
Velocity at Point 1: 5 m/s
Diameter at Point 2: .1 m
P = 300 kPa
Kinematic Viscosity: 1.12x10-6 m2/s
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
Velocity at Point 2: .1.26 m/s CONTINUITY:
Q = Av
AREA:
A1v1 = A2 v2
πd2 A= 4
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m
5 m/s
5 cm
10 cm
Velocity at Point 1: 5 m/s
Diameter at Point 2: .1 m
P = 300 kPa
Kinematic Viscosity: 1.12x10-6 m2/s
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
Velocity at Point 2: .1.26 m/s CONTINUITY:
Q = Av
AREA:
A1v1 = A2 v2
πd2 A= 4
π (.05)2 A1 = 4
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m
5 m/s
5 cm
10 cm
Velocity at Point 1: 5 m/s
Diameter at Point 2: .1 m
P = 300 kPa
Kinematic Viscosity: 1.12x10-6 m2/s
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
Velocity at Point 2: .1.26 m/s CONTINUITY:
Q = Av
AREA:
A1v1 = A2 v2
πd2 A= 4
π (.05)2 A1 = = .00198 m 2 4
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m Area at Point 1: .00198 m2
5 m/s
5 cm
10 cm
Velocity at Point 1: 5 m/s
Diameter at Point 2: .1 m
P = 300 kPa
Kinematic Viscosity: 1.12x10-6 m2/s
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
Area at Point 2: .00785 m2
Velocity at Point 2: .1.26 m/s CONTINUITY:
Q = Av
AREA:
A1v1 = A2 v2
πd2 A= 4
π (.05)2 A1 = = .00198 m 2 4
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m Area at Point 1: .00198 m2
5 m/s
5 cm
10 cm
Velocity at Point 1: 5 m/s
Diameter at Point 2: .1 m
P = 300 kPa
Kinematic Viscosity: 1.12x10-6 m2/s
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
Area at Point 2: .00785 m2
Velocity at Point 2: .1.26 m/s CONTINUITY:
Q = Av
AREA:
A1v1 = A2 v2
πd2 A= 4
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m Area at Point 1: .00198 m2
5 m/s
5 cm
10 cm
Velocity at Point 1: 5 m/s
Diameter at Point 2: .1 m
P = 300 kPa
Kinematic Viscosity: 1.12x10-6 m2/s
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
Area at Point 2: .00785 m2
Velocity at Point 2: .1.26 m/s CONTINUITY:
Q = Av
AREA:
A1v1 = A2 v2
πd2 A= 4
π (.1)2 A2 = 4
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m Area at Point 1: .00198 m2
5 m/s
5 cm
10 cm
Velocity at Point 1: 5 m/s
Diameter at Point 2: .1 m
P = 300 kPa
Kinematic Viscosity: 1.12x10-6 m2/s
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
Area at Point 2: .00785 m2
Velocity at Point 2: .1.26 m/s CONTINUITY:
Q = Av
AREA:
A1v1 = A2 v2
πd2 A= 4
π (.1)2 A2 = = .00785 m 2 4
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m Area at Point 1: .00198 m2
5 m/s
5 cm
10 cm
Velocity at Point 1: 5 m/s
Diameter at Point 2: .1 m
P = 300 kPa
Kinematic Viscosity: 1.12x10-6 m2/s
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
Area at Point 2: .00785 m2
Velocity at Point 2: .1.26 m/s CONTINUITY:
Q = Av
AREA:
A1v1 = A2 v2
πd2 A= 4
π (.1)2 A2 = = .00785 m 2 4
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m Area at Point 1: .00198 m2
5 m/s
5 cm
10 cm
Diameter at Point 2: .1 m
P = 300 kPa
vDρ vD Re = = µ υ
Area at Point 2: .00785 m2
Kinematic Viscosity: 1.12x10-6 m2/s
SOLUTION: REYNOLDS NUMBER:
Velocity at Point 1: 5 m/s
Velocity at Point 2: .1.26 m/s CONTINUITY:
Q = Av
A1v1 = A2 v2
.00198 m 2 (5 m/s) = .00785 m 2 (v2 )
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m Area at Point 1: .00198 m2
5 m/s
5 cm
10 cm
Diameter at Point 2: .1 m
P = 300 kPa
vDρ vD Re = = µ υ
Area at Point 2: .00785 m2
Kinematic Viscosity: 1.12x10-6 m2/s
SOLUTION: REYNOLDS NUMBER:
Velocity at Point 1: 5 m/s
Velocity at Point 2: .1.26 m/s CONTINUITY:
Q = Av
A1v1 = A2 v2
.00198 m 2 (5 m/s) = .00785 m 2 (v2 )
.00198 m 2 (5 m/s) v2 = .00785 m 2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m Area at Point 1: .00198 m2
5 m/s
5 cm
10 cm
Diameter at Point 2: .1 m
P = 300 kPa
vDρ vD Re = = µ υ
Area at Point 2: .00785 m2
Kinematic Viscosity: 1.12x10-6 m2/s
SOLUTION: REYNOLDS NUMBER:
Velocity at Point 1: 5 m/s
Velocity at Point 2: .1.26 m/s CONTINUITY:
Q = Av
A1v1 = A2 v2
.00198 m 2 (5 m/s) = .00785 m 2 (v2 )
.00198 m 2 (5 m/s) v2 = = 1.26 m/s 2 .00785 m
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m Area at Point 1: .00198 m2
5 m/s
5 cm
1.26 m/s
10 cm
Diameter at Point 2: .1 m
P = 300 kPa
vDρ vD Re = = µ υ
Area at Point 2: .00785 m2
Kinematic Viscosity: 1.12x10-6 m2/s
SOLUTION: REYNOLDS NUMBER:
Velocity at Point 1: 5 m/s
Velocity at Point 2: 1.26 m/s CONTINUITY:
Q = Av
A1v1 = A2 v2
.00198 m 2 (5 m/s) = .00785 m 2 (v2 )
.00198 m 2 (5 m/s) v2 = = 1.26 m/s 2 .00785 m
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m Area at Point 1: .00198 m2
5 m/s
5 cm
1.26 m/s
P = 300 kPa
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
10 cm
Velocity at Point 1: 5 m/s
Diameter at Point 2: .1 m
Area at Point 2: .00785 m2
Kinematic Viscosity: 1.12x10-6 m2/s
Velocity at Point 2: 1.26 m/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m Area at Point 1: .00198 m2
5 m/s
5 cm
1.26 m/s
P = 300 kPa
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
10 cm
Velocity at Point 1: 5 m/s
Diameter at Point 2: .1 m
Area at Point 2: .00785 m2
Kinematic Viscosity: 1.12x10-6 m2/s
Velocity at Point 2: 1.26 m/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m Area at Point 1: .00198 m2
5 m/s
5 cm
1.26 m/s
P = 300 kPa
SOLUTION: REYNOLDS NUMBER:
vDρ vD (1.26 m/s)(.1 m) Re = = = µ υ 1.12x10 -6 m 2 /s
10 cm
Velocity at Point 1: 5 m/s
Diameter at Point 2: .1 m
Area at Point 2: .00785 m2
Kinematic Viscosity: 1.12x10-6 m2/s
Velocity at Point 2: 1.26 m/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m Area at Point 1: .00198 m2
5 m/s
5 cm
1.26 m/s
P = 300 kPa
SOLUTION: REYNOLDS NUMBER:
vDρ vD (1.26 m/s)(.1 m) Re = = = = 112,500 -6 2 µ υ 1.12x10 m /s
10 cm
Velocity at Point 1: 5 m/s
Diameter at Point 2: .1 m
Area at Point 2: .00785 m2
Kinematic Viscosity: 1.12x10-6 m2/s
Velocity at Point 2: 1.26 m/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number after the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m Area at Point 1: .00198 m2
5 m/s
5 cm
1.26 m/s
10 cm
Diameter at Point 2: .1 m
P = 300 kPa
Area at Point 2: .00785 m2
Kinematic Viscosity: 1.12x10-6 m2/s
SOLUTION:
Velocity at Point 2: 1.26 m/s
REYNOLDS NUMBER:
vDρ vD (1.26 m/s)(.1 m) Re = = = = 112,500 -6 2 µ υ 1.12x10 m /s
Velocity at Point 1: 5 m/s
Re = 112,500
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number before the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m Area at Point 1: .00198 m2
5 m/s
5 cm
1.26 m/s
P = 300 kPa
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
10 cm
Velocity at Point 1: 5 m/s
Diameter at Point 2: .1 m
Area at Point 2: .00785 m2
Kinematic Viscosity: 1.12x10-6 m2/s
Velocity at Point 2: 1.26 m/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number before the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m Area at Point 1: .00198 m2
5 m/s
5 cm
1.26 m/s
P = 300 kPa
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
10 cm
Velocity at Point 1: 5 m/s
Diameter at Point 2: .1 m
Area at Point 2: .00785 m2
Kinematic Viscosity: 1.12x10-6 m2/s
Velocity at Point 2: 1.26 m/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number before the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m Area at Point 1: .00198 m2
5 m/s
5 cm
1.26 m/s
P = 300 kPa
SOLUTION: REYNOLDS NUMBER:
vDρ vD (5 m/s)(.05 m) Re = = = µ υ 1.12x10 -6 m 2 /s
10 cm
Velocity at Point 1: 5 m/s
Diameter at Point 2: .1 m
Area at Point 2: .00785 m2
Kinematic Viscosity: 1.12x10-6 m2/s
Velocity at Point 2: 1.26 m/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number before the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m Area at Point 1: .00198 m2
5 m/s
5 cm
1.26 m/s
P = 300 kPa
SOLUTION: REYNOLDS NUMBER:
vDρ vD (5 m/s)(.05 m) Re = = = = 223,214 -6 2 µ υ 1.12x10 m /s
10 cm
Velocity at Point 1: 5 m/s
Diameter at Point 2: .1 m
Area at Point 2: .00785 m2
Kinematic Viscosity: 1.12x10-6 m2/s
Velocity at Point 2: 1.26 m/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water is flowing in a 5 centimeter diameter pipe at a velocity of 5 m/s. If the pipe expands to a 10 centimeter diameter, and the kinematic viscosity after this expansion is 1.12 x 10-6 m2/s, the Reynolds number before the expansion is most close to:
B
GIVEN:
A
Diameter at Point 1: .05 m Area at Point 1: .00198 m2
5 m/s
5 cm
1.26 m/s
10 cm
Diameter at Point 2: .1 m
P = 300 kPa
Area at Point 2: .00785 m2
Kinematic Viscosity: 1.12x10-6 m2/s
SOLUTION:
Velocity at Point 2: 1.26 m/s
REYNOLDS NUMBER:
vDρ vD (5 m/s)(.05 m) Re = = = = 223,214 -6 2 µ υ 1.12x10 m /s
Velocity at Point 1: 5 m/s
Re = 223,214
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to:
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to:
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to:
CENTERLINE
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to:
25 mm CENTERLINE
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
CONSEQUENCES OF FLUID FLOW
CONSEQUENCES OF FLUID FLOW
The GENERAL PRINCIPLES revolving around the REYNOLDS NUMBER can be referenced on Page 105 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW
The GENERAL PRINCIPLES revolving around the REYNOLDS NUMBER can be referenced on Page 105 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to:
25 mm CENTERLINE
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to:
25 mm CENTERLINE
SOLUTION: REYNOLDS NUMBER: VELOCITY
vDρ vD Re = = µ υ
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to:
25 mm CENTERLINE
SOLUTION: DENSITY OF FLUID REYNOLDS NUMBER: VELOCITY
vDρ vD Re = = µ υ
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to:
25 mm CENTERLINE
SOLUTION: DENSITY OF FLUID REYNOLDS NUMBER: VELOCITY
vDρ vD Re = = µ υ
DIAMETER OF SECTION
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to:
25 mm CENTERLINE
SOLUTION: DENSITY OF FLUID REYNOLDS NUMBER: VELOCITY
vDρ vD Re = = µ υ
DIAMETER OF SECTION
KINEMATIC VISCOSITY
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to:
25 mm CENTERLINE
SOLUTION: DENSITY OF FLUID REYNOLDS NUMBER: VELOCITY
vDρ vD Re = = µ υ
DIAMETER OF SECTION
DYNAMIC VISCOSITY KINEMATIC VISCOSITY
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to: GIVEN:
25 mm CENTERLINE
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to: GIVEN: Diameter of Pipe: 150 mm
25 mm CENTERLINE
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
Average Velocity: 3.6 m/s
Temperature of Fluid: 25oC
Kinematic Viscosity: 7.63x10-4 m2/s
Reynolds Number: 708
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to: GIVEN: Diameter of Pipe: .15 m
25 mm CENTERLINE
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
Average Velocity: 3.6 m/s
Temperature of Fluid: 25oC
Kinematic Viscosity: 7.63x10-4 m2/s
Reynolds Number: 708
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to: GIVEN: Diameter of Pipe: .15 m
25 mm CENTERLINE
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
Average Velocity: 3.6 m/s
Temperature of Fluid: 25oC
Kinematic Viscosity: 7.63x10-4 m2/s
Reynolds Number: 708
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to: GIVEN: Diameter of Pipe: .15 m
25 mm CENTERLINE
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
Average Velocity: 3.6 m/s
Temperature of Fluid: 25oC
Kinematic Viscosity: 7.63x10-4 m2/s
Reynolds Number: 708
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to: GIVEN: Diameter of Pipe: .15 m
25 mm CENTERLINE
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
Average Velocity: 3.6 m/s
Temperature of Fluid: 25oC
Kinematic Viscosity: 7.63x10-4 m2/s
Reynolds Number: 708
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to: GIVEN: Diameter of Pipe: .15 m
25 mm CENTERLINE
SOLUTION: REYNOLDS NUMBER:
vDρ vD Re = = µ υ
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
Average Velocity: 3.6 m/s
Temperature of Fluid: 25oC
Kinematic Viscosity: 7.63x10-4 m2/s
Reynolds Number: 708
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to: GIVEN: Diameter of Pipe: .15 m
25 mm CENTERLINE
SOLUTION: REYNOLDS NUMBER:
vDρ vD (3.6 m/s)(.15 m) Re = = = µ υ 7.63x10 -4 m 2 /s
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
Average Velocity: 3.6 m/s
Temperature of Fluid: 25oC
Kinematic Viscosity: 7.63x10-4 m2/s
Reynolds Number: 708
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to: GIVEN: Diameter of Pipe: .15 m
25 mm CENTERLINE
SOLUTION: REYNOLDS NUMBER:
vDρ vD (3.6 m/s)(.15 m) Re = = = = 708 -4 2 µ υ 7.63x10 m /s
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
Average Velocity: 3.6 m/s
Temperature of Fluid: 25oC
Kinematic Viscosity: 7.63x10-4 m2/s
Reynolds Number: 708
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to: GIVEN: Diameter of Pipe: .15 m
25 mm CENTERLINE
SOLUTION: REYNOLDS NUMBER:
vDρ vD (3.6 m/s)(.15 m) Re = = = = 708 -4 2 µ υ 7.63x10 m /s
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
Average Velocity: 3.6 m/s
Temperature of Fluid: 25oC
Kinematic Viscosity: 7.63x10-4 m2/s
Reynolds Number: 708
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to: GIVEN: Diameter of Pipe: .15 m
25 mm CENTERLINE
SOLUTION:
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
Average Velocity: 3.6 m/s
Temperature of Fluid: 25oC
Kinematic Viscosity: 7.63x10-4 m2/s
Reynolds Number: 708
CONSEQUENCES OF FLUID FLOW
CONSEQUENCES OF FLUID FLOW
The GENERAL PRINCIPLES revolving around VELOCITY DISTRIBUTION can be referenced on Page 105 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW
The GENERAL PRINCIPLES revolving around VELOCITY DISTRIBUTION can be referenced on Page 105 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to: GIVEN: Diameter of Pipe: .15 m
25 mm CENTERLINE
SOLUTION: VELOCITY DISTRIBUTION:
⎡ ⎛ r ⎞2⎤ v(r) = vmax ⎢1− ⎥ ⎣ ⎝ R⎠ ⎦
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
Average Velocity: 3.6 m/s
Temperature of Fluid: 25oC
Kinematic Viscosity: 7.63x10-4 m2/s
Reynolds Number: 708
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to: GIVEN: Diameter of Pipe: .15 m
25 mm CENTERLINE
SOLUTION: DISTRIBUTION: VELOCITYVELOCITY AT SPECIFIED DISTANCE
⎡ ⎛ r ⎞2⎤ v(r) = vmax ⎢1− ⎥ ⎣ ⎝ R⎠ ⎦
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
Average Velocity: 3.6 m/s
Temperature of Fluid: 25oC
Kinematic Viscosity: 7.63x10-4 m2/s
Reynolds Number: 708
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to: GIVEN: Diameter of Pipe: .15 m
25 mm CENTERLINE
SOLUTION: DISTRIBUTION: VELOCITYVELOCITY AT SPECIFIED DISTANCE
⎡ ⎛ r ⎞2⎤ v(r) = vmax ⎢1− ⎥ DISTANCE FROM CENTERLINE ⎝ ⎠ R ⎣ ⎦
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
Average Velocity: 3.6 m/s
Temperature of Fluid: 25oC
Kinematic Viscosity: 7.63x10-4 m2/s
Reynolds Number: 708
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to: GIVEN: Diameter of Pipe: .15 m
25 mm CENTERLINE
SOLUTION: DISTRIBUTION: VELOCITYVELOCITY AT SPECIFIED DISTANCE
⎡ ⎛ r ⎞2⎤ v(r) = vmax ⎢1− ⎥ DISTANCE FROM CENTERLINE ⎝ ⎠ R ⎣ ⎦
RADIUS OF PIPE
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
Average Velocity: 3.6 m/s
Temperature of Fluid: 25oC
Kinematic Viscosity: 7.63x10-4 m2/s
Reynolds Number: 708
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to: GIVEN: Diameter of Pipe: .15 m
25 mm CENTERLINE
SOLUTION: DISTRIBUTION: VELOCITYVELOCITY AT SPECIFIED DISTANCE
⎡ ⎛ r ⎞2⎤ v(r) = vmax ⎢1− ⎥ DISTANCE FROM CENTERLINE ⎝ ⎠ R ⎣ ⎦ MAXIMUM VELOCITY RADIUS OF PIPE
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
Average Velocity: 3.6 m/s
Temperature of Fluid: 25oC
Kinematic Viscosity: 7.63x10-4 m2/s
Reynolds Number: 708
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to: GIVEN: Diameter of Pipe: .15 m
25 mm CENTERLINE
SOLUTION: DISTRIBUTION: VELOCITYVELOCITY AT SPECIFIED DISTANCE
⎡ ⎛ r ⎞2⎤ v(r) = vmax ⎢1− ⎥ DISTANCE FROM CENTERLINE ⎝ ⎠ R ⎣ ⎦ MAXIMUM VELOCITY RADIUS OF PIPE
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
Average Velocity: 3.6 m/s
Temperature of Fluid: 25oC
Kinematic Viscosity: 7.63x10-4 m2/s
Reynolds Number: 708
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to: GIVEN: Diameter of Pipe: .15 m
25 mm CENTERLINE
SOLUTION: VELOCITY DISTRIBUTION:
⎡ ⎛ r ⎞2⎤ v(r) = vmax ⎢1− ⎥ ⎣ ⎝ R⎠ ⎦
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
Average Velocity: 3.6 m/s
Temperature of Fluid: 25oC
Kinematic Viscosity: 7.63x10-4 m2/s
Reynolds Number: 708
CONSEQUENCES OF FLUID FLOW
CONSEQUENCES OF FLUID FLOW
The GENERAL PRINCIPLES revolving around VELOCITY DISTRIBUTION can be referenced on Page 105 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to: GIVEN: Diameter of Pipe: .15 m
25 mm CENTERLINE
SOLUTION: VELOCITY DISTRIBUTION:
⎡ ⎛ r ⎞2⎤ v(r) = vmax ⎢1− ⎥ ⎣ ⎝ R⎠ ⎦
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
Average Velocity: 3.6 m/s
Temperature of Fluid: 25oC
Kinematic Viscosity: 7.63x10-4 m2/s
Reynolds Number: 708
MAXIMUM VELOCITY:
vmax = 2v
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to: GIVEN: Diameter of Pipe: .15 m
25 mm CENTERLINE
SOLUTION: VELOCITY DISTRIBUTION:
⎡ ⎛ r ⎞2⎤ v(r) = vmax ⎢1− ⎥ ⎣ ⎝ R⎠ ⎦
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
Average Velocity: 3.6 m/s
Temperature of Fluid: 25oC
Kinematic Viscosity: 7.63x10-4 m2/s
Reynolds Number: 708
MAXIMUM VELOCITY:
vmax = 2v = 2(3.6 m/s)
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to: GIVEN: Diameter of Pipe: .15 m
25 mm CENTERLINE
SOLUTION: VELOCITY DISTRIBUTION:
⎡ ⎛ r ⎞2⎤ v(r) = vmax ⎢1− ⎥ ⎣ ⎝ R⎠ ⎦
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
Average Velocity: 3.6 m/s
Temperature of Fluid: 25oC
Kinematic Viscosity: 7.63x10-4 m2/s
Reynolds Number: 708
MAXIMUM VELOCITY:
vmax = 2v = 2(3.6 m/s) = 7.2 m/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to: GIVEN: Diameter of Pipe: .15 m
25 mm CENTERLINE
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
Average Velocity: 3.6 m/s
Temperature of Fluid: 25oC
Kinematic Viscosity: 7.63x10-4 m2/s
SOLUTION:
Reynolds Number: 708
VELOCITY DISTRIBUTION:
Maximum Velocity: 7.2 m/s
⎡ ⎛ r ⎞2⎤ v(r) = vmax ⎢1− ⎥ ⎣ ⎝ R⎠ ⎦
MAXIMUM VELOCITY:
vmax = 2v = 2(3.6 m/s) = 7.2 m/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to: GIVEN: Diameter of Pipe: .15 m
25 mm CENTERLINE
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
Average Velocity: 3.6 m/s
Temperature of Fluid: 25oC
Kinematic Viscosity: 7.63x10-4 m2/s
SOLUTION:
Reynolds Number: 708
VELOCITY DISTRIBUTION:
Maximum Velocity: 7.2 m/s
⎡ ⎛ r ⎞2⎤ v(r) = vmax ⎢1− ⎥ ⎣ ⎝ R⎠ ⎦
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to: GIVEN: Diameter of Pipe: .15 m
25 mm CENTERLINE
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
Average Velocity: 3.6 m/s
Temperature of Fluid: 25oC
Kinematic Viscosity: 7.63x10-4 m2/s
SOLUTION:
Reynolds Number: 708
VELOCITY DISTRIBUTION:
Maximum Velocity: 7.2 m/s
⎡ ⎛ r ⎞2⎤ v(r) = vmax ⎢1− ⎥ ⎣ ⎝ R⎠ ⎦
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to: GIVEN: Diameter of Pipe: .15 m
25 mm CENTERLINE
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
Average Velocity: 3.6 m/s
Temperature of Fluid: 25oC
Kinematic Viscosity: 7.63x10-4 m2/s
SOLUTION:
Reynolds Number: 708
VELOCITY DISTRIBUTION:
Maximum Velocity: 7.2 m/s
⎡ ⎛ r ⎞2⎤ ⎡ ⎛ .25 m ⎞ 2 ⎤ v(r) = vmax ⎢1− = 7.2 m/s ⎢1− = 6.4 m/s ⎥ ⎥ ⎣ ⎝ R⎠ ⎦ ⎣ ⎝ .75 m ⎠ ⎦
CONSEQUENCES OF FLUID FLOW EXAMPLE: Glycerin at 25oC flows through a pipe with a 150 millimeter inside diameter. If the kinematic viscosity and average velocity of this fluid at the centerline of flow are 7.63 x 10-4 m2/s and 3.6 m/s respectively, the velocity a distance of 25 millimeters from this centerline is most close to: GIVEN: Diameter of Pipe: .15 m
25 mm CENTERLINE
T = 25oC
v = 3.6 m/s
! = 7.63 m2/s
Average Velocity: 3.6 m/s
Temperature of Fluid: 25oC
Kinematic Viscosity: 7.63x10-4 m2/s
SOLUTION:
Reynolds Number: 708
VELOCITY DISTRIBUTION:
Maximum Velocity: 7.2 m/s
⎡ ⎛ r ⎞2⎤ ⎡ ⎛ .25 m ⎞ 2 ⎤ v(r) = vmax ⎢1− = 7.2 m/s ⎢1− = 6.4 m/s ⎥ ⎥ ⎣ ⎝ R⎠ ⎦ ⎣ ⎝ .75 m ⎠ ⎦
v = 6.4 m/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: A
WATER P
FEED ELEVATION = 23 ft
DISCHARGE ELEVATION = 33 ft
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: A
WATER P
FEED ELEVATION = 23 ft
DISCHARGE ELEVATION = 33 ft
CONSEQUENCES OF FLUID FLOW
CONSEQUENCES OF FLUID FLOW
The DARCY-WEISBACH EQUATION can be referenced on Page 106 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: A
WATER P
SOLUTION: DARCY-WEISBACH EQUATION:
L v2 hf = f D 2g
FEED ELEVATION = 23 ft
DISCHARGE ELEVATION = 33 ft
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: A
WATER P
SOLUTION: DARCY-WEISBACH EQUATION: HEAD LOSS
L v2 hf = f D 2g
FEED ELEVATION = 23 ft
DISCHARGE ELEVATION = 33 ft
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: A
WATER P
SOLUTION: FRICTION FACTOR DARCY-WEISBACH EQUATION: HEAD LOSS
L v2 hf = f D 2g
FEED ELEVATION = 23 ft
DISCHARGE ELEVATION = 33 ft
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: A
WATER P
SOLUTION: FRICTION FACTOR DARCY-WEISBACH EQUATION: HEAD LOSS
L v2 hf = f D 2g
LENGTH OF PIPE RUN
FEED ELEVATION = 23 ft
DISCHARGE ELEVATION = 33 ft
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: A
WATER P
SOLUTION: FRICTION FACTOR DARCY-WEISBACH EQUATION: HEAD LOSS
L v2 hf = f D 2g
LENGTH OF PIPE RUN VELOCITY
FEED ELEVATION = 23 ft
DISCHARGE ELEVATION = 33 ft
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: A
WATER P
SOLUTION: FRICTION FACTOR DARCY-WEISBACH EQUATION: HEAD LOSS
L v2 hf = f D 2g
LENGTH OF PIPE RUN VELOCITY
LOCAL GRAVITY
FEED ELEVATION = 23 ft
DISCHARGE ELEVATION = 33 ft
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: A
WATER P
SOLUTION: FRICTION FACTOR DARCY-WEISBACH EQUATION: HEAD LOSS
L v2 hf = f D 2g DIAMETER OF PIPE LOCAL GRAVITY
LENGTH OF PIPE RUN VELOCITY
FEED ELEVATION = 23 ft
DISCHARGE ELEVATION = 33 ft
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: GIVEN: A
WATER P
SOLUTION: DARCY-WEISBACH EQUATION:
L v2 hf = f D 2g
FEED ELEVATION = 23 ft
DISCHARGE ELEVATION = 33 ft
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: GIVEN: A
WATER
DISCHARGE ELEVATION = 33 ft
Diameter of Pipe: .083 ft
Flow Rate of Fluid: 50 gpm
P
FEED ELEVATION = 23 ft
Temperature of Fluid: 60oF
Length of Pipe: 50 ft
SOLUTION:
Area of Pipe: .0054 ft2
DARCY-WEISBACH EQUATION:
Velocity in Pipe: 20.7 ft/s
L v2 hf = f D 2g
Kinematic Viscosity: 1.217x10-5 ft2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: GIVEN: A
WATER
DISCHARGE ELEVATION = 33 ft
Diameter of Pipe: .083 ft
Flow Rate of Fluid: 50 gpm
P
FEED ELEVATION = 23 ft
Temperature of Fluid: 60oF
Length of Pipe: 50 ft
SOLUTION:
Area of Pipe: .0054 ft2
DARCY-WEISBACH EQUATION:
Velocity in Pipe: 20.7 ft/s
L v2 hf = f D 2g
Kinematic Viscosity: 1.217x10-5 ft2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: GIVEN: A
DISCHARGE ELEVATION = 33 ft
WATER
Diameter of Pipe: .083 ft
Flow Rate of Fluid: 50 gpm
P
FEED ELEVATION = 23 ft
Temperature of Fluid: 60oF
Length of Pipe: 50 ft
SOLUTION: DARCY-WEISBACH EQUATION:
L v2 hf = f D 2g
Area of Pipe: .0054 ft2
CONVERSION FROM gpm TO ft3/s:
Velocity in Pipe: 20.7 ft/s
Kinematic Viscosity: 1.217x10-5 ft2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: GIVEN: A
DISCHARGE ELEVATION = 33 ft
WATER
Diameter of Pipe: .083 ft
Flow Rate of Fluid: 50 gpm
P
FEED ELEVATION = 23 ft
Temperature of Fluid: 60oF
Length of Pipe: 50 ft
SOLUTION: DARCY-WEISBACH EQUATION:
L v2 hf = f D 2g
Area of Pipe: .0054 ft2
CONVERSION FROM gpm TO ft3/s:
Gal ⎛ .134 ft 3 ⎞ ⎛ 1 min ⎞ 50 min ⎜⎝ 1 Gal ⎟⎠ ⎝ 60 s ⎠
Velocity in Pipe: 20.7 ft/s
Kinematic Viscosity: 1.217x10-5 ft2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: GIVEN: A
DISCHARGE ELEVATION = 33 ft
WATER
Diameter of Pipe: .083 ft
Flow Rate of Fluid: .112 ft3/s
P
FEED ELEVATION = 23 ft
Temperature of Fluid: 60oF
Length of Pipe: 50 ft
SOLUTION: DARCY-WEISBACH EQUATION:
L v2 hf = f D 2g
Area of Pipe: .0054 ft2
CONVERSION FROM gpm TO ft3/s:
Gal ⎛ .134 ft 3 ⎞ ⎛ 1 min ⎞ 3 50 = .112 ft /s ⎜ ⎟ min ⎝ 1 Gal ⎠ ⎝ 60 s ⎠
Velocity in Pipe: 20.7 ft/s
Kinematic Viscosity: 1.217x10-5 ft2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: GIVEN: A
WATER
DISCHARGE ELEVATION = 33 ft
Diameter of Pipe: .083 ft
Flow Rate of Fluid: .112 ft3/s
P
FEED ELEVATION = 23 ft
Temperature of Fluid: 60oF
Length of Pipe: 50 ft
SOLUTION:
Area of Pipe: .0054 ft2
DARCY-WEISBACH EQUATION:
Velocity in Pipe: 20.7 ft/s
L v2 hf = f D 2g
Kinematic Viscosity: 1.217x10-5 ft2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: GIVEN: A
WATER
DISCHARGE ELEVATION = 33 ft
Diameter of Pipe: .083 ft
Flow Rate of Fluid: .112 ft3/s
P
FEED ELEVATION = 23 ft
Temperature of Fluid: 60oF
Length of Pipe: 50 ft
SOLUTION:
Area of Pipe: .0054 ft2
DARCY-WEISBACH EQUATION:
Velocity in Pipe: 20.7 ft/s
L v2 hf = f D 2g
Kinematic Viscosity: 1.217x10-5 ft2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: GIVEN: A
WATER
DISCHARGE ELEVATION = 33 ft
Diameter of Pipe: .083 ft
Flow Rate of Fluid: .112 ft3/s
P
FEED ELEVATION = 23 ft
Temperature of Fluid: 60oF
Length of Pipe: 50 ft
SOLUTION: DARCY-WEISBACH EQUATION:
L v2 hf = f D 2g
Area of Pipe: .0054 ft2
CONTINUITY:
Velocity in Pipe: 20.7 ft/s
Kinematic Viscosity: 1.217x10-5 ft2/s
Q = Av
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: GIVEN: A
WATER
DISCHARGE ELEVATION = 33 ft
Diameter of Pipe: .083 ft
Flow Rate of Fluid: .112 ft3/s
P
FEED ELEVATION = 23 ft
Temperature of Fluid: 60oF
Length of Pipe: 50 ft
SOLUTION: DARCY-WEISBACH EQUATION:
L v2 hf = f D 2g
Area of Pipe: .0054 ft2
CONTINUITY:
Velocity in Pipe: 20.7 ft/s
Kinematic Viscosity: 1.217x10-5 ft2/s
Q = Av AREA:
πd A= 4
2
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: GIVEN: A
WATER
DISCHARGE ELEVATION = 33 ft
Diameter of Pipe: .083 ft
Flow Rate of Fluid: .112 ft3/s
P
FEED ELEVATION = 23 ft
Temperature of Fluid: 60oF
Length of Pipe: 50 ft
SOLUTION: DARCY-WEISBACH EQUATION:
L v2 hf = f D 2g
Area of Pipe: .0054 ft2
Velocity in Pipe: 20.7 ft/s
CONTINUITY:
Kinematic Viscosity: 1.217x10-5 ft2/s
Q = Av AREA:
πd A= 4
2
π (.083 ft) A= 4
2
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: GIVEN: A
DISCHARGE ELEVATION = 33 ft
WATER
Diameter of Pipe: .083 ft
Flow Rate of Fluid: .112 ft3/s
P
FEED ELEVATION = 23 ft
Temperature of Fluid: 60oF
Length of Pipe: 50 ft
SOLUTION: DARCY-WEISBACH EQUATION:
L v2 hf = f D 2g
Area of Pipe: .0054 ft2
Velocity in Pipe: 20.7 ft/s
CONTINUITY:
Kinematic Viscosity: 1.217x10-5 ft2/s
Q = Av AREA:
πd A= 4
2
π (.083 ft) 2 A= = .0054 ft 4 2
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: GIVEN: A
DISCHARGE ELEVATION = 33 ft
WATER
Diameter of Pipe: .083 ft
Flow Rate of Fluid: .112 ft3/s
P
FEED ELEVATION = 23 ft
Temperature of Fluid: 60oF
Length of Pipe: 50 ft
SOLUTION: DARCY-WEISBACH EQUATION:
L v2 hf = f D 2g
Area of Pipe: .0054 ft2
Velocity in Pipe: 20.7 ft/s
CONTINUITY:
Kinematic Viscosity: 1.217x10-5 ft2/s
Q = Av AREA:
πd A= 4
2
π (.083 ft) 2 A= = .0054 ft 4 2
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: GIVEN: A
DISCHARGE ELEVATION = 33 ft
WATER
Diameter of Pipe: .083 ft
Flow Rate of Fluid: .112 ft3/s
P
FEED ELEVATION = 23 ft
Temperature of Fluid: 60oF
Length of Pipe: 50 ft
SOLUTION: DARCY-WEISBACH EQUATION:
L v2 hf = f D 2g
Area of Pipe: .0054 ft2
Velocity in Pipe: 20.7 ft/s
CONTINUITY:
Kinematic Viscosity: 1.217x10-5 ft2/s
Q = Av
.112 ft 3 /s = (.0054 ft 2 )v
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: GIVEN: A
DISCHARGE ELEVATION = 33 ft
WATER
Diameter of Pipe: .083 ft
Flow Rate of Fluid: .112 ft3/s
FEED ELEVATION = 23 ft
P
Temperature of Fluid: 60oF
Length of Pipe: 50 ft
SOLUTION: DARCY-WEISBACH EQUATION:
L v2 hf = f D 2g
Area of Pipe: .0054 ft2
Velocity in Pipe: 20.7 ft/s
CONTINUITY:
Kinematic Viscosity: 1.217x10-5 ft2/s
Q = Av
.112 ft 3 /s = (.0054 ft 2 )v
.112 ft 3 /s v= (.0054 m 2 )
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: GIVEN: A
DISCHARGE ELEVATION = 33 ft
WATER
Diameter of Pipe: .083 ft
Flow Rate of Fluid: .112 ft3/s
P
FEED ELEVATION = 23 ft
Temperature of Fluid: 60oF
Length of Pipe: 50 ft
SOLUTION: DARCY-WEISBACH EQUATION:
L v2 hf = f D 2g
Area of Pipe: .0054 ft2
Velocity in Pipe: 20.7 ft/s
CONTINUITY:
Kinematic Viscosity: 1.217x10-5 ft2/s
Q = Av
.112 ft 3 /s = (.0054 ft 2 )v
.112 ft 3 /s v= = 20.7 ft/s 2 (.0054 m )
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: GIVEN: A
DISCHARGE ELEVATION = 33 ft
WATER
Diameter of Pipe: .083 ft
Flow Rate of Fluid: .112 ft3/s
P
FEED ELEVATION = 23 ft
Temperature of Fluid: 60oF
Length of Pipe: 50 ft
SOLUTION: DARCY-WEISBACH EQUATION:
L v2 hf = f D 2g
Area of Pipe: .0054 ft2
Velocity in Pipe: 20.7 ft/s
CONTINUITY:
Kinematic Viscosity: 1.217x10-5 ft2/s
Q = Av
.112 ft 3 /s = (.0054 ft 2 )v
.112 ft 3 /s v= = 20.7 ft/s 2 (.0054 m )
CONSEQUENCES OF FLUID FLOW
CONSEQUENCES OF FLUID FLOW
PROPERTIES OF WATER at various temperatures can be referenced on Page 114 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW
PROPERTIES OF WATER at various temperatures can be referenced on Page 114 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: GIVEN: A
WATER
DISCHARGE ELEVATION = 33 ft
Diameter of Pipe: .083 ft
Flow Rate of Fluid: .112 ft3/s
P
FEED ELEVATION = 23 ft
Temperature of Fluid: 60oF
Length of Pipe: 50 ft
SOLUTION:
Area of Pipe: .0054 ft2
DARCY-WEISBACH EQUATION:
Velocity in Pipe: 20.7 ft/s
L v2 hf = f D 2g
Kinematic Viscosity: 1.217x10-5 ft2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: GIVEN: A
WATER
DISCHARGE ELEVATION = 33 ft
Diameter of Pipe: .083 ft
Flow Rate of Fluid: .112 ft3/s
P
FEED ELEVATION = 23 ft
Temperature of Fluid: 60oF
Length of Pipe: 50 ft
SOLUTION:
Area of Pipe: .0054 ft2
DARCY-WEISBACH EQUATION:
Velocity in Pipe: 20.7 ft/s
L v2 hf = f D 2g
REYNOLDS NUMBER:
vDρ vD Re = = µ υ
Kinematic Viscosity: 1.217x10-5 ft2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: GIVEN: A
WATER
DISCHARGE ELEVATION = 33 ft
Diameter of Pipe: .083 ft
Flow Rate of Fluid: .112 ft3/s
P
FEED ELEVATION = 23 ft
Temperature of Fluid: 60oF
Length of Pipe: 50 ft
SOLUTION:
Area of Pipe: .0054 ft2
DARCY-WEISBACH EQUATION:
Velocity in Pipe: 20.7 ft/s
L v2 hf = f D 2g
REYNOLDS NUMBER:
vDρ vD Re = = µ υ
Kinematic Viscosity: 1.217x10-5 ft2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: GIVEN: A
DISCHARGE ELEVATION = 33 ft
WATER
Diameter of Pipe: .083 ft
Flow Rate of Fluid: .112 ft3/s
P
FEED ELEVATION = 23 ft
Temperature of Fluid: 60oF
Length of Pipe: 50 ft
SOLUTION:
Area of Pipe: .0054 ft2
DARCY-WEISBACH EQUATION:
Velocity in Pipe: 20.7 ft/s
L v2 hf = f D 2g
REYNOLDS NUMBER:
vDρ vD (20.7 ft/s)(.083 ft) Re = = = µ υ 1.217x10 -5 ft 2 /s
Kinematic Viscosity: 1.217x10-5 ft2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: GIVEN: A
DISCHARGE ELEVATION = 33 ft
WATER
Diameter of Pipe: .083 ft
Flow Rate of Fluid: .112 ft3/s
P
FEED ELEVATION = 23 ft
Temperature of Fluid: 60oF
Length of Pipe: 50 ft
SOLUTION:
Area of Pipe: .0054 ft2
DARCY-WEISBACH EQUATION:
Velocity in Pipe: 20.7 ft/s
L v2 hf = f D 2g
REYNOLDS NUMBER:
vDρ vD (20.7 ft/s)(.083 ft) Re = = = = 141,175 -5 2 µ υ 1.217x10 ft /s
Kinematic Viscosity: 1.217x10-5 ft2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: GIVEN: A
DISCHARGE ELEVATION = 33 ft
WATER
Diameter of Pipe: .083 ft
Flow Rate of Fluid: .112 ft3/s
P
FEED ELEVATION = 23 ft
Temperature of Fluid: 60oF
Length of Pipe: 50 ft
SOLUTION:
Area of Pipe: .0054 ft2
DARCY-WEISBACH EQUATION:
Velocity in Pipe: 20.7 ft/s
L v2 hf = f D 2g
REYNOLDS NUMBER:
vDρ vD (20.7 ft/s)(.083 ft) Re = = = = 141,175 -5 2 µ υ 1.217x10 ft /s
Kinematic Viscosity: 1.217x10-5 ft2/s
Reynolds Number: 141,175
CONSEQUENCES OF FLUID FLOW
The MOODY (STANTON) DIAGRAM can be referenced on Page 115 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW
The MOODY (STANTON) DIAGRAM can be referenced on Page 115 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW
The MOODY (STANTON) DIAGRAM can be referenced on Page 115 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW
The MOODY (STANTON) DIAGRAM can be referenced on Page 115 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW
.018 .016
The MOODY (STANTON) DIAGRAM can be referenced on Page 115 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW
.0162
The MOODY (STANTON) DIAGRAM can be referenced on Page 115 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: GIVEN: A
WATER
DISCHARGE ELEVATION = 33 ft
Diameter of Pipe: .083 ft
Flow Rate of Fluid: .112 ft3/s
P
FEED ELEVATION = 23 ft
Temperature of Fluid: 60oF
Length of Pipe: 50 ft
SOLUTION:
Area of Pipe: .0054 ft2
DARCY-WEISBACH EQUATION:
Velocity in Pipe: 20.7 ft/s
L v2 hf = f D 2g
Kinematic Viscosity: 1.217x10-5 ft2/s
Reynolds Number: 141,175
Friction Factor: .0162
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: GIVEN: A
WATER
DISCHARGE ELEVATION = 33 ft
Diameter of Pipe: .083 ft
Flow Rate of Fluid: .112 ft3/s
P
FEED ELEVATION = 23 ft
Temperature of Fluid: 60oF
Length of Pipe: 50 ft
SOLUTION:
Area of Pipe: .0054 ft2
DARCY-WEISBACH EQUATION:
Velocity in Pipe: 20.7 ft/s
L v2 hf = f D 2g
Kinematic Viscosity: 1.217x10-5 ft2/s
Reynolds Number: 141,175
Friction Factor: .0162
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: GIVEN: A
WATER
DISCHARGE ELEVATION = 33 ft
Diameter of Pipe: .083 ft
Flow Rate of Fluid: .112 ft3/s
P
FEED ELEVATION = 23 ft
Temperature of Fluid: 60oF
Length of Pipe: 50 ft
SOLUTION:
Area of Pipe: .0054 ft2
DARCY-WEISBACH EQUATION:
Velocity in Pipe: 20.7 ft/s
L v2 hf = f D 2g
Kinematic Viscosity: 1.217x10-5 ft2/s
Reynolds Number: 141,175
Friction Factor: .0162
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: GIVEN: A
WATER
DISCHARGE ELEVATION = 33 ft
Diameter of Pipe: .083 ft
Flow Rate of Fluid: .112 ft3/s
P
FEED ELEVATION = 23 ft
Temperature of Fluid: 60oF
Length of Pipe: 50 ft
SOLUTION:
Area of Pipe: .0054 ft2
DARCY-WEISBACH EQUATION:
Velocity in Pipe: 20.7 ft/s
2 ⎛ ⎞ L v2 50 ft (20.7 ft/s) ⎛ ⎞ hf = f = .0162 2 ⎟ ⎜ ⎝ ⎠ D 2g .083 ft ⎝ 2(32.2 ft/s ) ⎠
Kinematic Viscosity: 1.217x10-5 ft2/s
Reynolds Number: 141,175
Friction Factor: .0162
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: GIVEN: A
WATER
DISCHARGE ELEVATION = 33 ft
Diameter of Pipe: .083 ft
Flow Rate of Fluid: .112 ft3/s
P
FEED ELEVATION = 23 ft
Temperature of Fluid: 60oF
Length of Pipe: 50 ft
SOLUTION:
Area of Pipe: .0054 ft2
DARCY-WEISBACH EQUATION:
Velocity in Pipe: 20.7 ft/s
2 ⎛ ⎞ L v2 50 ft (20.7 ft/s) ⎛ ⎞ hf = f = .0162 = 64.9 ft 2 ⎟ ⎜ ⎝ .083 ft ⎠ ⎝ 2(32.2 ft/s ) ⎠ D 2g
Kinematic Viscosity: 1.217x10-5 ft2/s
Reynolds Number: 141,175
Friction Factor: .0162
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: A pump is used to deliver 50 gpm of 60oF water from a holding tank through 50 ft of smooth piping with a diameter of 1 inch. If the fluid exits at the elevation noted and the contraction ratio is assumed to be very large, the head loss due to friction along the pipe run is most close to: GIVEN: A
DISCHARGE ELEVATION = 33 ft
WATER
Diameter of Pipe: .083 ft
Flow Rate of Fluid: .112 ft3/s
P
FEED ELEVATION = 23 ft
Temperature of Fluid: 60oF
Length of Pipe: 50 ft
SOLUTION:
Area of Pipe: .0054 ft2
DARCY-WEISBACH EQUATION:
Velocity in Pipe: 20.7 ft/s
2 ⎛ ⎞ L v2 50 ft (20.7 ft/s) ⎛ ⎞ hf = f = .0162 = 64.9 ft 2 ⎟ ⎜ ⎝ .083 ft ⎠ ⎝ 2(32.2 ft/s ) ⎠ D 2g
Kinematic Viscosity: 1.217x10-5 ft2/s
hf = 64.9 ft
Reynolds Number: 141,175
Friction Factor: .0162
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 217 ft, the head loss due to friction along the pipe run is most close to: WATER P
DISCHARGE ELEVATION = 10 ft
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: WATER P
DISCHARGE ELEVATION = 10 ft
CONSEQUENCES OF FLUID FLOW
CONSEQUENCES OF FLUID FLOW
The DARCY-WEISBACH EQUATION can be referenced on Page 106 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: WATER P
SOLUTION: DARCY-WEISBACH EQUATION:
L v2 hf = f D 2g
DISCHARGE ELEVATION = 10 ft
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: WATER P
SOLUTION: DARCY-WEISBACH EQUATION: HEAD LOSS
L v2 hf = f D 2g
DISCHARGE ELEVATION = 10 ft
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: WATER P
SOLUTION: FRICTION FACTOR DARCY-WEISBACH EQUATION: HEAD LOSS
L v2 hf = f D 2g
DISCHARGE ELEVATION = 10 ft
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: WATER P
SOLUTION: FRICTION FACTOR DARCY-WEISBACH EQUATION: HEAD LOSS
L v2 hf = f D 2g
LENGTH OF PIPE RUN
DISCHARGE ELEVATION = 10 ft
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: WATER P
SOLUTION: FRICTION FACTOR DARCY-WEISBACH EQUATION: HEAD LOSS
L v2 hf = f D 2g
LENGTH OF PIPE RUN VELOCITY
DISCHARGE ELEVATION = 10 ft
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: WATER P
SOLUTION: FRICTION FACTOR DARCY-WEISBACH EQUATION: HEAD LOSS
L v2 hf = f D 2g
LENGTH OF PIPE RUN VELOCITY
LOCAL GRAVITY
DISCHARGE ELEVATION = 10 ft
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: WATER P
SOLUTION: FRICTION FACTOR DARCY-WEISBACH EQUATION: HEAD LOSS
L v2 hf = f D 2g DIAMETER OF PIPE LOCAL GRAVITY
LENGTH OF PIPE RUN VELOCITY
DISCHARGE ELEVATION = 10 ft
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER P
SOLUTION: DARCY-WEISBACH EQUATION:
L v2 hf = f D 2g
DISCHARGE ELEVATION = 10 ft
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 3.35 ft3/s
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION:
Pipe Roughness: .0004 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .785 ft2
L v2 hf = f D 2g
Velocity in Pipe: 4.26 ft/s
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
Friction Factor: .0173
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 1500 gpm
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION:
Pipe Roughness: .0004 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .785 ft2
L v2 hf = f D 2g
Velocity in Pipe: 4.26 ft/s
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
Friction Factor: .0173
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 1500 gpm
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION: DARCY-WEISBACH EQUATION:
L v2 hf = f D 2g
Pipe Roughness: .0004 ft
CONVERSION FROM gpm TO
ft3/s:
Area of Pipe: .785 ft2
Velocity in Pipe: 4.26 ft/s
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
Friction Factor: .0173
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 1500 gpm
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION: DARCY-WEISBACH EQUATION:
L v2 hf = f D 2g
Pipe Roughness: .0004 ft
CONVERSION FROM gpm TO
Gal ⎛ .134 ft 3 ⎞ ⎛ 1 min ⎞ 1500 min ⎜⎝ 1 Gal ⎟⎠ ⎝ 60 s ⎠
ft3/s:
Area of Pipe: .785 ft2
Velocity in Pipe: 4.26 ft/s
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
Friction Factor: .0173
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 3.35 ft3/s
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION: DARCY-WEISBACH EQUATION:
L v2 hf = f D 2g
Pipe Roughness: .0004 ft
CONVERSION FROM gpm TO
ft3/s:
Gal ⎛ .134 ft 3 ⎞ ⎛ 1 min ⎞ 3 1500 = 3.35 ft /s ⎜ ⎟ min ⎝ 1 Gal ⎠ ⎝ 60 s ⎠
Area of Pipe: .785 ft2
Velocity in Pipe: 4.26 ft/s
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
Friction Factor: .0173
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 3.35 ft3/s
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION:
Pipe Roughness: .0004 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .785 ft2
L v2 hf = f D 2g
Velocity in Pipe: 4.26 ft/s
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
Friction Factor: .0173
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 3.35 ft3/s
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION:
Pipe Roughness: .0004 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .785 ft2
L v2 hf = f D 2g
Velocity in Pipe: 4.26 ft/s
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
Friction Factor: .0173
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 3.35 ft3/s
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION:
Pipe Roughness: .0004 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .785 ft2
L v2 hf = f D 2g
Velocity in Pipe: 4.26 ft/s
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
Friction Factor: .0173
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 3.35 ft3/s
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION:
Pipe Roughness: .0004 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .785 ft2
L v2 hf = f D 2g
CONTINUITY:
Velocity in Pipe: 4.26 ft/s
Q = Av
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
Friction Factor: .0173
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 3.35 ft3/s
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION:
Pipe Roughness: .0004 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .785 ft2
L v2 hf = f D 2g
CONTINUITY:
Velocity in Pipe: 4.26 ft/s
Q = Av
Reynolds Number: 402,266
AREA:
πd A= 4
Kinematic Viscosity: 1.059x10-5 ft2/s
Friction Factor: .0173
2
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 3.35 ft3/s
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION:
Pipe Roughness: .0004 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .785 ft2
L v2 hf = f D 2g
CONTINUITY:
Velocity in Pipe: 4.26 ft/s
Q = Av
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
AREA:
πd A= 4
Friction Factor: .0173
2
π (1 ft) A= 4
2
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 3.35 ft3/s
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION:
Pipe Roughness: .0004 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .785 ft2
L v2 hf = f D 2g
CONTINUITY:
Velocity in Pipe: 4.26 ft/s
Q = Av
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
AREA:
πd A= 4
Friction Factor: .0173
2
π (1 ft) 2 A= = .785 ft 4 2
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 3.35 ft3/s
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION:
Pipe Roughness: .0004 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .785 ft2
L v2 hf = f D 2g
CONTINUITY:
Velocity in Pipe: 4.26 ft/s
Q = Av
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
AREA:
πd A= 4
Friction Factor: .0173
2
π (1 ft) 2 A= = .785 ft 4 2
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 3.35 ft3/s
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION:
Pipe Roughness: .0004 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .785 ft2
L v2 hf = f D 2g
CONTINUITY:
Velocity in Pipe: 4.26 ft/s
Q = Av
3.35 ft 3 /s = (.785 ft 2 )v
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
Friction Factor: .0173
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 3.35 ft3/s
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION:
Pipe Roughness: .0004 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .785 ft2
L v2 hf = f D 2g
CONTINUITY:
Velocity in Pipe: 4.26 ft/s
Q = Av
3.35 ft 3 /s = (.785 ft 2 )v
3.35 ft 3 /s v= (.785 m 2 )
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
Friction Factor: .0173
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 3.35 ft3/s
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION:
Pipe Roughness: .0004 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .785 ft2
L v2 hf = f D 2g
CONTINUITY:
Velocity in Pipe: 4.26 ft/s
Q = Av
3.35 ft 3 /s = (.785 ft 2 )v
3.35 ft 3 /s v= = 4.26 ft/s 2 (.785 m )
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
Friction Factor: .0173
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 3.35 ft3/s
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION:
Pipe Roughness: .0004 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .785 ft2
L v2 hf = f D 2g
CONTINUITY:
Velocity in Pipe: 4.26 ft/s
Q = Av
3.35 ft 3 /s = (.785 ft 2 )v
3.35 ft 3 /s v= = 4.26 ft/s 2 (.785 m )
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
Friction Factor: .0173
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW
CONSEQUENCES OF FLUID FLOW
PROPERTIES OF WATER at various temperatures can be referenced on Page 114 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW
PROPERTIES OF WATER at various temperatures can be referenced on Page 114 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 3.35 ft3/s
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION:
Pipe Roughness: .0004 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .785 ft2
L v2 hf = f D 2g
Velocity in Pipe: 4.26 ft/s
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
Friction Factor: .0173
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 3.35 ft3/s
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION:
Pipe Roughness: .0004 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .785 ft2
L v2 hf = f D 2g
REYNOLDS NUMBER:
vDρ vD Re = = µ υ
Velocity in Pipe: 4.26 ft/s
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
Friction Factor: .0173
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 3.35 ft3/s
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION:
Pipe Roughness: .0004 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .785 ft2
L v2 hf = f D 2g
REYNOLDS NUMBER:
vDρ vD Re = = µ υ
Velocity in Pipe: 4.26 ft/s
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
Friction Factor: .0173
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 3.35 ft3/s
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION:
Pipe Roughness: .0004 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .785 ft2
L v2 hf = f D 2g
REYNOLDS NUMBER:
vDρ vD (4.26 ft/s)(1 ft) Re = = = µ υ 1.059x10 -5 ft 2 /s
Velocity in Pipe: 4.26 ft/s
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
Friction Factor: .0173
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 3.35 ft3/s
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION:
Pipe Roughness: .0004 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .785 ft2
L v2 hf = f D 2g
REYNOLDS NUMBER:
vDρ vD (4.26 ft/s)(1 ft) Re = = = = 402,266 -5 2 µ υ 1.059x10 ft /s
Velocity in Pipe: 4.26 ft/s
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
Friction Factor: .0173
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 3.35 ft3/s
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION:
Pipe Roughness: .0004 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .785 ft2
L v2 hf = f D 2g
REYNOLDS NUMBER:
vDρ vD (4.26 ft/s)(1 ft) Re = = = = 402,266 -5 2 µ υ 1.059x10 ft /s
Velocity in Pipe: 4.26 ft/s
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
Friction Factor: .0173
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW
The MOODY (STANTON) DIAGRAM can be referenced on Page 115 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW
The MOODY (STANTON) DIAGRAM can be referenced on Page 115 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 3.35 ft3/s
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION:
Pipe Roughness: .0004 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .785 ft2
L v2 hf = f D 2g
RELATIVE ROUGHNESS:
ε D
Velocity in Pipe: 4.26 ft/s
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
Friction Factor: .0173
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 3.35 ft3/s
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION:
Pipe Roughness: .0004 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .785 ft2
L v2 hf = f D 2g
RELATIVE ROUGHNESS:
ε D
Velocity in Pipe: 4.26 ft/s
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
Friction Factor: .0173
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 3.35 ft3/s
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION:
Pipe Roughness: .0004 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .785 ft2
L v2 hf = f D 2g
RELATIVE ROUGHNESS:
ε .0004 ft = D 1 ft
Velocity in Pipe: 4.26 ft/s
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
Friction Factor: .0173
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 3.35 ft3/s
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION:
Pipe Roughness: .0004 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .785 ft2
L v2 hf = f D 2g
RELATIVE ROUGHNESS:
ε .0004 ft = = .0004 D 1 ft
Velocity in Pipe: 4.26 ft/s
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
Friction Factor: .0173
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW
The MOODY (STANTON) DIAGRAM can be referenced on Page 115 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW
The MOODY (STANTON) DIAGRAM can be referenced on Page 115 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW
The MOODY (STANTON) DIAGRAM can be referenced on Page 115 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW
The MOODY (STANTON) DIAGRAM can be referenced on Page 115 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW
.018 .016
The MOODY (STANTON) DIAGRAM can be referenced on Page 115 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW
.0173
The MOODY (STANTON) DIAGRAM can be referenced on Page 115 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 3.35 ft3/s
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION:
Pipe Roughness: .0004 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .785 ft2
L v2 hf = f D 2g
Velocity in Pipe: 4.26 ft/s
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
Friction Factor: .0173
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 3.35 ft3/s
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION:
Pipe Roughness: .0004 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .785 ft2
L v2 hf = f D 2g
Velocity in Pipe: 4.26 ft/s
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
Friction Factor: .0173
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 3.35 ft3/s
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION:
Pipe Roughness: .0004 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .785 ft2
L v2 hf = f D 2g
Velocity in Pipe: 4.26 ft/s
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
Friction Factor: .0173
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 3.35 ft3/s
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION:
Pipe Roughness: .0004 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .785 ft2
2 ⎛ ⎞ L v2 507 ft (4.26 ft/s) ⎛ ⎞ hf = f = .0173 2 ⎟ ⎜ ⎝ ⎠ D 2g 1 ft ⎝ 2(32.2 ft/s ) ⎠
Velocity in Pipe: 4.26 ft/s
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
Friction Factor: .0173
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 3.35 ft3/s
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION:
Pipe Roughness: .0004 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .785 ft2
2 ⎛ ⎞ L v2 507 ft (4.26 ft/s) ⎛ ⎞ hf = f = .0173 = 2.47 ft 2 ⎟ ⎜ ⎝ 1 ft ⎠ ⎝ 2(32.2 ft/s ) ⎠ D 2g
Velocity in Pipe: 4.26 ft/s
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
Friction Factor: .0173
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: An asphalted cast iron pipe (ε = .0004) with a 1 ft diameter delivers 1500 gpm of 70oF water from a holding tank. If the fluid exits at the elevation noted and the length of the pipe is measured at 507 ft, the head loss due to friction along the pipe run is most close to: GIVEN: WATER
Diameter of Pipe: 1 ft
P
DISCHARGE ELEVATION = 10 ft
Flow Rate of Fluid: 3.35 ft3/s
Temperature of Fluid: 70oF
Length of Pipe: 507 ft
SOLUTION:
Pipe Roughness: .0004 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .785 ft2
2 ⎛ ⎞ L v2 507 ft (4.26 ft/s) ⎛ ⎞ hf = f = .0173 = 2.47 ft 2 ⎟ ⎜ ⎝ 1 ft ⎠ ⎝ 2(32.2 ft/s ) ⎠ D 2g
Velocity in Pipe: 4.26 ft/s
hf = 2.47 ft
Kinematic Viscosity: 1.059x10-5 ft2/s
Reynolds Number: 402,266
Friction Factor: .0173
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
CONSEQUENCES OF FLUID FLOW
CONSEQUENCES OF FLUID FLOW
The DARCY-WEISBACH EQUATION can be referenced on Page 106 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW
The DARCY-WEISBACH EQUATION can be referenced on Page 106 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
SOLUTION: DARCY-WEISBACH EQUATION:
L v2 hf = f D 2g
Exit, C = 1.06
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
SOLUTION: DARCY-WEISBACH EQUATION: HEAD LOSS
L v2 hf = f D 2g
Exit, C = 1.06
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
SOLUTION: FRICTION FACTOR DARCY-WEISBACH EQUATION: HEAD LOSS
L v2 hf = f D 2g
Exit, C = 1.06
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
SOLUTION: FRICTION FACTOR DARCY-WEISBACH EQUATION: HEAD LOSS
L v2 hf = f D 2g
LENGTH OF PIPE RUN
Exit, C = 1.06
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
SOLUTION: FRICTION FACTOR DARCY-WEISBACH EQUATION: HEAD LOSS
L v2 hf = f D 2g
LENGTH OF PIPE RUN VELOCITY
Exit, C = 1.06
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
SOLUTION: FRICTION FACTOR DARCY-WEISBACH EQUATION: HEAD LOSS
L v2 hf = f D 2g
LENGTH OF PIPE RUN VELOCITY
LOCAL GRAVITY
Exit, C = 1.06
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
SOLUTION: FRICTION FACTOR DARCY-WEISBACH EQUATION: HEAD LOSS
L v2 hf = f D 2g DIAMETER OF PIPE LOCAL GRAVITY
LENGTH OF PIPE RUN VELOCITY
Exit, C = 1.06
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
SOLUTION: DARCY-WEISBACH EQUATION:
L v2 hf = f D 2g
GIVEN:
Exit, C = 1.06
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .0218 ft2
L v2 hf = f D 2g
Velocity in Pipe: 9.72 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 115,123
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: 1.6 gpm
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .0218 ft2
L v2 hf = f D 2g
Velocity in Pipe: 9.72 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 115,123
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
GIVEN:
CAST IRON (ε = .00085 ft)
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: 1.6 gpm
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION: DARCY-WEISBACH EQUATION:
L v2 hf = f D 2g
Pipe Roughness: .00085 ft
CONVERSION FROM gpm TO
ft3/s:
Area of Pipe: .0218 ft2
Velocity in Pipe: 9.72 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 115,123
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
GIVEN:
CAST IRON (ε = .00085 ft)
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: 1.6 gpm
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION: DARCY-WEISBACH EQUATION:
L v2 hf = f D 2g
Pipe Roughness: .00085 ft
CONVERSION FROM gpm TO
Gal ⎛ .134 ft 3 ⎞ ⎛ 1 min ⎞ 1.6 min ⎜⎝ 1 Gal ⎟⎠ ⎝ 60 s ⎠
ft3/s:
Area of Pipe: .0218 ft2
Velocity in Pipe: 9.72 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 115,123
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
GIVEN:
CAST IRON (ε = .00085 ft)
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION: DARCY-WEISBACH EQUATION:
L v2 hf = f D 2g
Pipe Roughness: .00085 ft
CONVERSION FROM gpm TO
ft3/s:
Gal ⎛ .134 ft 3 ⎞ ⎛ 1 min ⎞ 3 1.6 = .212 ft /s ⎜ ⎟ min ⎝ 1 Gal ⎠ ⎝ 60 s ⎠
Area of Pipe: .0218 ft2
Velocity in Pipe: 9.72 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 115,123
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .0218 ft2
L v2 hf = f D 2g
Velocity in Pipe: 9.72 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 115,123
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .0218 ft2
L v2 hf = f D 2g
Velocity in Pipe: 9.72 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 115,123
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .0218 ft2
L v2 hf = f D 2g
Velocity in Pipe: 9.72 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 115,123
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .0219 ft2
L v2 hf = f D 2g
CONTINUITY:
Velocity in Pipe: 9.72 ft/s
Q = Av
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 115,123
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .0219 ft2
L v2 hf = f D 2g
CONTINUITY:
Velocity in Pipe: 9.72 ft/s
Q = Av
Reynolds Number: 115,123
AREA:
πd A= 4
Kinematic Viscosity: 1.41x10-5 ft2/s
Friction Factor: .03
2
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .0219 ft2
L v2 hf = f D 2g
CONTINUITY:
Velocity in Pipe: 9.72 ft/s
Q = Av
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 115,123
AREA:
πd A= 4
Friction Factor: .03
2
π (.167 ft) A= 4
2
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
GIVEN:
CAST IRON (ε = .00085 ft)
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .0219 ft2
L v2 hf = f D 2g
CONTINUITY:
Velocity in Pipe: 9.72 ft/s
Q = Av
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 115,123
AREA:
πd A= 4
Friction Factor: .03
2
π (.167 ft) 2 A= = .0219 ft 4 2
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
GIVEN:
CAST IRON (ε = .00085 ft)
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .0219 ft2
L v2 hf = f D 2g
CONTINUITY:
Velocity in Pipe: 9.72 ft/s
Q = Av
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 115,123
AREA:
πd A= 4
Friction Factor: .03
2
π (.167 ft) 2 A= = .0219 ft 4 2
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
GIVEN:
CAST IRON (ε = .00085 ft)
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .0219 ft2
L v2 hf = f D 2g
CONTINUITY:
Velocity in Pipe: 9.68 ft/s
Q = Av
.212 ft 3 /s = (.0219 ft 2 )v
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 115,123
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
GIVEN:
CAST IRON (ε = .00085 ft)
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .0219 ft2
L v2 hf = f D 2g
CONTINUITY:
Velocity in Pipe: 9.68 ft/s
Q = Av
.212 ft 3 /s = (.0219 ft 2 )v
.212 ft 3 /s v= (.0219 m 2 )
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 115,123
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
GIVEN:
CAST IRON (ε = .00085 ft)
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .0219 ft2
L v2 hf = f D 2g
CONTINUITY:
Velocity in Pipe: 9.68 ft/s
Q = Av
.212 ft 3 /s = (.0219 ft 2 )v
.212 ft 3 /s v= = 9.68 ft/s 2 (.0219 m )
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 115,123
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
GIVEN:
CAST IRON (ε = .00085 ft)
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .0219 ft2
L v2 hf = f D 2g
CONTINUITY:
Velocity in Pipe: 9.68 ft/s
Q = Av
.212 ft 3 /s = (.0219 ft 2 )v
.212 ft 3 /s v= = 9.68 ft/s 2 (.0219 m )
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 115,123
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW
CONSEQUENCES OF FLUID FLOW
PROPERTIES OF WATER at various temperatures can be referenced on Page 114 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW
PROPERTIES OF WATER at various temperatures can be referenced on Page 114 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .0219 ft2
L v2 hf = f D 2g
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 115,123
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .0219 ft2
L v2 hf = f D 2g
REYNOLDS NUMBER:
vDρ vD Re = = µ υ
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .0219 ft2
L v2 hf = f D 2g
REYNOLDS NUMBER:
vDρ vD Re = = µ υ
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
GIVEN:
CAST IRON (ε = .00085 ft)
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .0219 ft2
L v2 hf = f D 2g
REYNOLDS NUMBER:
vDρ vD (9.68 ft/s)(.167 ft) Re = = = µ υ 1.41x10 -5 ft 2 /s
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .0219 ft2
L v2 hf = f D 2g
REYNOLDS NUMBER:
Velocity in Pipe: 9.68 ft/s
vDρ vD (9.68 ft/s)(.167 ft) -5 ft2/s
Re = = = = 114,650 Kinematic Viscosity: 1.41x10 µ υ 1.41x10 -5 ft 2 /s Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .0219 ft2
L v2 hf = f D 2g
REYNOLDS NUMBER:
Velocity in Pipe: 9.68 ft/s
vDρ vD (9.68 ft/s)(.167 ft) -5 ft2/s
Re = = = = 114,650 Kinematic Viscosity: 1.41x10 µ υ 1.41x10 -5 ft 2 /s Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW
The MOODY (STANTON) DIAGRAM can be referenced on Page 115 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW
The MOODY (STANTON) DIAGRAM can be referenced on Page 115 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .0219 ft2
L v2 hf = f D 2g
RELATIVE ROUGHNESS:
ε D
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .0219 ft2
L v2 hf = f D 2g
RELATIVE ROUGHNESS:
ε D
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .0219 ft2
L v2 hf = f D 2g
RELATIVE ROUGHNESS:
ε .00085 ft = D .167 ft
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .0219 ft2
L v2 hf = f D 2g
RELATIVE ROUGHNESS:
ε .00085 ft = = .005 D .167 ft
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW
The MOODY (STANTON) DIAGRAM can be referenced on Page 115 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW
The MOODY (STANTON) DIAGRAM can be referenced on Page 115 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW
The MOODY (STANTON) DIAGRAM can be referenced on Page 115 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW
The MOODY (STANTON) DIAGRAM can be referenced on Page 115 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .0219 ft2
L v2 hf = f D 2g
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .0219 ft2
L v2 hf = f D 2g
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .0219 ft2
L v2 hf = f D 2g
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .0219 ft2
2 ⎛ ⎞ L v2 290 ft (9.68 ft/s) ⎛ ⎞ hf = f = .03 2 ⎟ ⎜ ⎝ ⎠ D 2g .167 ft ⎝ 2(32.2 ft/s ) ⎠
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION:
Area of Pipe: .0219 ft2
2 ⎛ ⎞ L v2 290 ft (9.68 ft/s) ⎛ ⎞ hf = f = .03 = 75.6 ft 2 ⎟ ⎜ ⎝ .167 ft ⎠ ⎝ 2(32.2 ft/s ) ⎠ D 2g
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION: 75.6 ft
Area of Pipe: .0219 ft2
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW
The DARCY-WEISBACH EQUATION can be referenced on Page 106 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION: 75.6 ft
Area of Pipe: .0219 ft2
Velocity in Pipe: 9.68 ft/s
MINOR LOSSES:
h f , fitting
v2 =C 2g
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION: 75.6 ft
Area of Pipe: .0219 ft2
Velocity in Pipe: 9.68 ft/s
MINOR LOSSES: HEAD LOSS
h f , fitting
v2 =C 2g
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION: 75.6 ft
Area of Pipe: .0219 ft2
LOSS COEFFICIENT MINOR LOSSES: HEAD LOSS
h f , fitting
v2 =C 2g
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION: 75.6 ft
Area of Pipe: .0219 ft2
LOSS COEFFICIENT MINOR LOSSES: HEAD LOSS VELOCITY 2 v h f , fitting = C 2g
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION: 75.6 ft
Area of Pipe: .0219 ft2
LOSS COEFFICIENT MINOR LOSSES: HEAD LOSS VELOCITY 2 v h f , fitting = C 2g LOCAL GRAVITY
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION: 75.6 ft
Area of Pipe: .0219 ft2
Velocity in Pipe: 9.68 ft/s
MINOR LOSSES:
h f , fitting
v2 =C 2g
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION: 75.6 ft
Area of Pipe: .0219 ft2
Velocity in Pipe: 9.68 ft/s
MINOR LOSSES:
h f , fitting
v2 =C 2g
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
GIVEN:
CAST IRON (ε = .00085 ft)
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION: 75.6 ft
Area of Pipe: .0219 ft2
Velocity in Pipe: 9.68 ft/s
MINOR LOSSES:
h f , fitting
Kinematic Viscosity: 1.41x10-5 ft2/s
⎛ (9.86 m/s)2 ⎞ ⎛ (9.86 m/s)2 ⎞ ⎛ (9.86 m/s)2 ⎞ v2 =C = (.5) ⎜ + (.3) ⎜ + (.3) ⎜ 2 ⎟ 2 ⎟ 2 ⎟ 2g 2(32.2 m/s ) 2(32.2 m/s ) 2(32.2 m/s )⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎛ (9.86 m/s)2 ⎞ ⎛ (9.86 m/s)2 ⎞ +(.2) ⎜ + (1.06) ⎜ 2 ⎟ ⎝ 2(32.2 m/s ) ⎠ ⎝ 2(32.2 m/s 2 ) ⎟⎠
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION: 75.6 ft
Area of Pipe: .0219 ft2
Velocity in Pipe: 9.68 ft/s
MINOR LOSSES:
h f , fitting
⎛ (9.86 m/s)2 ⎞ v2 =C = (.5 + .3 + .3 + .2 + 1.06) ⎜ 2 ⎟ 2g 2(32.2 m/s )⎠ ⎝
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION: 75.6 ft
Area of Pipe: .0219 ft2
Velocity in Pipe: 9.68 ft/s
MINOR LOSSES:
h f , fitting
⎛ (9.86 m/s)2 ⎞ v2 =C = (.5 + .3 + .3 + .2 + 1.06) ⎜ = 3.56 ft 2 ⎟ 2g ⎝ 2(32.2 m/s ) ⎠
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION: 75.6 ft
Area of Pipe: .0219 ft2
Velocity in Pipe: 9.68 ft/s
MINOR LOSSES: 3.56 ft
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION: 75.6 ft
Area of Pipe: .0219 ft2
Velocity in Pipe: 9.68 ft/s
MINOR LOSSES: 3.56 ft TOTAL HEAD LOSS: 75.6 ft + 3.56 ft
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION: 75.6 ft
Area of Pipe: .0219 ft2
Velocity in Pipe: 9.68 ft/s
MINOR LOSSES: 3.56 ft TOTAL HEAD LOSS: 75.6 ft + 3.56 ft = 79.16 ft
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
GIVEN:
CAST IRON (ε = .00085 ft)
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
DARCY-WEISBACH EQUATION: 75.6 ft
Area of Pipe: .0219 ft2
Velocity in Pipe: 9.68 ft/s
MINOR LOSSES: 3.56 ft TOTAL HEAD LOSS: 75.6 ft + 3.56 ft = 79.16 ft
Kinematic Viscosity: 1.41x10-5 ft2/s
hf,total = 79.2 ft
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW
The DARCY-WEISBACH EQUATION can be referenced on Page 106 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION: ENERGY EQUATION:
P1 (v1 )2 P2 (v2 )2 + z1 + = + z2 + + h f + h f , fitting γ 2g γ 2g
Pipe Roughness: .00085 ft
Area of Pipe: .0219 ft2
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION: PRESSURE AT POINT 1 ENERGY EQUATION:
P1 (v1 )2 P2 (v2 )2 + z1 + = + z2 + + h f + h f , fitting γ 2g γ 2g
Pipe Roughness: .00085 ft
Area of Pipe: .0219 ft2
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION: VELOCITY AT POINT 1 PRESSURE AT POINT 1 ENERGY EQUATION:
P1 (v1 )2 P2 (v2 )2 + z1 + = + z2 + + h f + h f , fitting γ 2g γ 2g
Pipe Roughness: .00085 ft
Area of Pipe: .0219 ft2
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION: VELOCITY AT POINT 1 PRESSURE AT POINT 1 ENERGY EQUATION: PRESSURE AT POINT 2
P1 (v1 )2 P2 (v2 )2 + z1 + = + z2 + + h f + h f , fitting γ 2g γ 2g
Pipe Roughness: .00085 ft
Area of Pipe: .0219 ft2
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION: VELOCITY AT POINT 1 PRESSURE AT POINT 1 ENERGY EQUATION: PRESSURE AT POINT 2 VELOCITY AT POINT 2 2 2 P1 (v1 ) P2 (v2 ) + z1 + = + z2 + + h f + h f , fitting γ 2g γ 2g
Pipe Roughness: .00085 ft
Area of Pipe: .0219 ft2
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION: VELOCITY AT POINT 1 PRESSURE AT POINT 1 ENERGY EQUATION: PRESSURE AT POINT 2 VELOCITY AT POINT 2 2 2 P1 (v1 ) P2 (v2 ) + z1 + = + z2 + + h f + h f , fitting MINOR LOSSES γ 2g γ 2g
Pipe Roughness: .00085 ft
Area of Pipe: .0219 ft2
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
VELOCITY AT POINT 1 PRESSURE AT POINT 1 ENERGY EQUATION: PRESSURE AT POINT 2 VELOCITY AT POINT 2 2 2 P1 (v1 ) P2 (v2 ) + z1 + = + z2 + + h f + h f , fitting MINOR LOSSES γ 2g γ 2g MAJOR LOSSES
Area of Pipe: .0219 ft2
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
VELOCITY AT POINT 1 PRESSURE AT POINT 1 ENERGY EQUATION: PRESSURE AT POINT 2 VELOCITY AT POINT 2 2 2 P1 (v1 ) P2 (v2 ) + z1 + = + z2 + + h f + h f , fitting MINOR LOSSES γ 2g γ 2g MAJOR LOSSES ELEVATION AT POINT 2
Area of Pipe: .0219 ft2
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
VELOCITY AT POINT 1 PRESSURE AT POINT 1 ENERGY EQUATION: PRESSURE AT POINT 2 VELOCITY AT POINT 2 2 2 P1 (v1 ) P2 (v2 ) + z1 + = + z2 + + h f + h f , fitting MINOR LOSSES γ 2g γ 2g MAJOR LOSSES ELEVATION AT POINT 2 LOCAL GRAVITY
Area of Pipe: .0219 ft2
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
VELOCITY AT POINT 1 PRESSURE AT POINT 1 ENERGY EQUATION: PRESSURE AT POINT 2 VELOCITY AT POINT 2 2 2 P1 (v1 ) P2 (v2 ) + z1 + = + z2 + + h f + h f , fitting MINOR LOSSES γ 2g γ 2g MAJOR LOSSES ELEVATION AT POINT 2
ELEVATION AT POINT 1 LOCAL GRAVITY
Area of Pipe: .0219 ft2
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
VELOCITY AT POINT 1 PRESSURE AT POINT 1 ENERGY EQUATION: PRESSURE AT POINT 2 VELOCITY AT POINT 2 2 2 P1 (v1 ) P2 (v2 ) + z1 + = + z2 + + h f + h f , fitting MINOR LOSSES γ 2g γ 2g SPECIFIC WEIGHT
MAJOR LOSSES ELEVATION AT POINT 2
ELEVATION AT POINT 1 LOCAL GRAVITY
Area of Pipe: .0219 ft2
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION: ENERGY EQUATION:
P1 (v1 )2 P2 (v2 )2 + z1 + = + z2 + + h f + h f , fitting γ 2g γ 2g
Pipe Roughness: .00085 ft
Area of Pipe: .0219 ft2
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION: ENERGY EQUATION:
P1 (v1 )2 P2 (v2 )2 + z1 + = + z2 + + h f + h f , fitting γ 2g γ 2g
Pipe Roughness: .00085 ft
Area of Pipe: .0219 ft2
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION: ENERGY EQUATION:
P1 (v1 )2 P2 (v2 )2 + z1 + = + z2 + + h f + h f , fitting γ 2g γ 2g
Pipe Roughness: .00085 ft
Area of Pipe: .0219 ft2
Velocity in Pipe: 9.68 ft/s
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION: ENERGY EQUATION:
Pipe Roughness: .00085 ft
Area of Pipe: .0219 ft2
Velocity in Pipe: 9.68 ft/s
z1 = z2 + h f + h f , fitting
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION: ENERGY EQUATION:
Pipe Roughness: .00085 ft
Area of Pipe: .0219 ft2
Velocity in Pipe: 9.68 ft/s
z1 = z2 + h f , total
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION: ENERGY EQUATION:
Pipe Roughness: .00085 ft
Area of Pipe: .0219 ft2
Velocity in Pipe: 9.68 ft/s
h f , total = z1 − z2
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION: ENERGY EQUATION:
Pipe Roughness: .00085 ft
Area of Pipe: .0219 ft2
Velocity in Pipe: 9.68 ft/s
h f , total = z1 − z2 = 92 ft − 13 ft = 79 ft
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 50oF flows from a large reservoir to a small reservoir through a 2 inch in diameter cast iron piping system. If the flow rate is 1.6 gpm, the total head loss along the pipe run, including fittings, is most close to: Sharp-Edged Entrance, C = .5
RESERVOIR 1 ELEVATION = 92 ft
CAST IRON (ε = .00085 ft)
GIVEN:
Standard Flanged Elbow, C = .3 Gate Valve, Fully Open, C = .2
30 ft
RESERVOIR 2 ELEVATION = 13 ft
WATER 260 ft
Exit, C = 1.06
Diameter of Pipe: .167 ft
Flow Rate of Fluid: .212 ft3/s
Temperature of Fluid: 50oF
Length of Pipe: 290 ft
SOLUTION:
Pipe Roughness: .00085 ft
Area of Pipe: .0219 ft2
ENERGY EQUATION:
Velocity in Pipe: 9.68 ft/s
h f , total = z1 − z2 = 92 ft − 13 ft = 79 ft
hf,total = 79 ft
Kinematic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 114,650
Friction Factor: .03
Local Gravity: 32.2 ft/s2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: WATER DISCHARGE ELEVATION = 15 ft
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: WATER DISCHARGE ELEVATION = 15 ft
CONSEQUENCES OF FLUID FLOW
CONSEQUENCES OF FLUID FLOW
The driving formula for determining the PRESSURE DROP FOR LAMINAR FLOW can be referenced on Page 106 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: WATER DISCHARGE ELEVATION = 15 ft
SOLUTION: HAGEN-POISEUILLE EQUATION:
π R 4 ΔPf π D 4 ΔPf Q= = 8µL 128 µ L
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: WATER DISCHARGE ELEVATION = 15 ft
SOLUTION: HAGEN-POISEUILLE EQUATION: FLOW RATE
π R 4 ΔPf π D 4 ΔPf Q= = 8µL 128 µ L
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: WATER DISCHARGE ELEVATION = 15 ft
SOLUTION: RADIUSEQUATION: OF SECTION HAGEN-POISEUILLE FLOW RATE
π R 4 ΔPf π D 4 ΔPf Q= = 8µL 128 µ L
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: WATER DISCHARGE ELEVATION = 15 ft
SOLUTION: RADIUSEQUATION: OF SECTION HAGEN-POISEUILLE FLOW RATE DIAMETER OF SECTION 4 4 π R ΔPf π D ΔPf Q= = 8µL 128 µ L
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: WATER DISCHARGE ELEVATION = 15 ft
SOLUTION: RADIUSEQUATION: OF SECTION HAGEN-POISEUILLE FLOW RATE DIAMETER OF SECTION 4 4 π R ΔPf π D ΔPf Q= = 8µL 128 µ L PRESSURE DROP
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: WATER DISCHARGE ELEVATION = 15 ft
SOLUTION: RADIUSEQUATION: OF SECTION HAGEN-POISEUILLE FLOW RATE DIAMETER OF SECTION 4 4 π R ΔPf π D ΔPf Q= = 8µL 128 µ L PRESSURE DROP LENGTH OF PIPE
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: WATER DISCHARGE ELEVATION = 15 ft
SOLUTION: RADIUSEQUATION: OF SECTION HAGEN-POISEUILLE FLOW RATE DIAMETER OF SECTION 4 4 π R ΔPf π D ΔPf Q= = 8µL 128 µ L PRESSURE DROP DYNAMIC VISCOSITY LENGTH OF PIPE
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
SOLUTION: HAGEN-POISEUILLE EQUATION:
π R 4 ΔPf π D 4 ΔPf Q= = 8µL 128 µ L
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .12 in
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION:
Kinematic Viscosity: 1.664x10-5 ft2/s
HAGEN-POISEUILLE EQUATION:
Area of Pipe: .000079 ft2
π R 4 ΔPf π D 4 ΔPf Q= = 8µL 128 µ L
Flow Rate of Fluid: .000237 ft3/s
Absolute Dynamic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 1,802
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION:
Kinematic Viscosity: 1.664x10-5 ft2/s
HAGEN-POISEUILLE EQUATION:
Area of Pipe: .000079 ft2
π R 4 ΔPf π D 4 ΔPf Q= = 8µL 128 µ L
Flow Rate of Fluid: .000237 ft3/s
Absolute Dynamic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 1,802
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION:
Kinematic Viscosity: 1.664x10-5 ft2/s
HAGEN-POISEUILLE EQUATION:
Area of Pipe: .000079 ft2
π R 4 ΔPf π D 4 ΔPf Q= = 8µL 128 µ L
Flow Rate of Fluid: .000237 ft3/s
Absolute Dynamic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 1,802
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION:
Kinematic Viscosity: 1.664x10-5 ft2/s
HAGEN-POISEUILLE EQUATION:
Area of Pipe: .000079 ft2
π R 4 ΔPf π D 4 ΔPf Q= = 8µL 128 µ L
Flow Rate of Fluid: .000237 ft3/s
Absolute Dynamic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 1,802
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION:
Kinematic Viscosity: 1.664x10-5 ft2/s
HAGEN-POISEUILLE EQUATION:
Area of Pipe: .000079 ft2
π R 4 ΔPf π D 4 ΔPf Q= = 8µL 128 µ L
Flow Rate of Fluid: .000237 ft3/s
Absolute Dynamic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 1,802
CONSEQUENCES OF FLUID FLOW
CONSEQUENCES OF FLUID FLOW
PROPERTIES OF WATER at various temperatures can be referenced on Page 114 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW
PROPERTIES OF WATER at various temperatures can be referenced on Page 114 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION:
Kinematic Viscosity: 1.664x10-5 ft2/s
HAGEN-POISEUILLE EQUATION:
Area of Pipe: .000079 ft2
π R 4 ΔPf π D 4 ΔPf Q= = 8µL 128 µ L
Flow Rate of Fluid: .000237 ft3/s
Absolute Dynamic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 1,802
CONSEQUENCES OF FLUID FLOW
The driving formula for determining the PRESSURE DROP FOR LAMINAR FLOW can be referenced on Page 106 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION:
Kinematic Viscosity: 1.664x10-5 ft2/s
REYNOLDS NUMBER:
Area of Pipe: .000079 ft2
vDρ vD Re = = µ υ
Flow Rate of Fluid: .000237 ft3/s
Absolute Dynamic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 1,802
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION:
Kinematic Viscosity: 1.664x10-5 ft2/s
DENSITY OF FLUID REYNOLDS NUMBER: VELOCITY
vDρ vD Re = = µ υ
Area of Pipe: .000079 ft2
Flow Rate of Fluid: .000237 ft3/s
DIAMETER OF SECTION
DYNAMIC VISCOSITY KINEMATIC VISCOSITY
Absolute Dynamic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 1,802
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION:
Kinematic Viscosity: 1.664x10-5 ft2/s
DENSITY OF FLUID REYNOLDS NUMBER: VELOCITY
vDρ vD Re = = µ υ
Area of Pipe: .000079 ft2
Flow Rate of Fluid: .000237 ft3/s
DIAMETER OF SECTION
DYNAMIC VISCOSITY KINEMATIC VISCOSITY
Absolute Dynamic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 1,802
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION:
Kinematic Viscosity: 1.664x10-5 ft2/s
REYNOLDS NUMBER:
Area of Pipe: .000079 ft2
vDρ vD Re = = µ υ
Flow Rate of Fluid: .000237 ft3/s
Absolute Dynamic Viscosity: 1.41x10-5 ft2/s
Reynolds Number: 1,802
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION:
Kinematic Viscosity: 1.664x10-5 ft2/s
REYNOLDS NUMBER:
Reynolds Number: 1,802
vDρ vD (3 ft/s)(.01 ft) Re = = = µ υ 1.664x10 −5 ft 2 /s
Area of Pipe: .000079 ft2
Flow Rate of Fluid: .000237 ft3/s
Absolute Dynamic Viscosity: 1.41x10-5 ft2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION:
Kinematic Viscosity: 1.664x10-5 ft2/s
REYNOLDS NUMBER:
Reynolds Number: 1,802
vDρ vD (3 ft/s)(.01 ft) Re = = = = 1,802 −5 2 µ υ 1.664x10 ft /s
Area of Pipe: .000079 ft2
Flow Rate of Fluid: .000237 ft3/s
Absolute Dynamic Viscosity: 1.41x10-5 ft2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION:
Kinematic Viscosity: 1.664x10-5 ft2/s
REYNOLDS NUMBER:
Reynolds Number: 1,802
vDρ vD (3 ft/s)(.01 ft) Re = = = = 1,802 −5 2 µ υ 1.664x10 ft /s
Area of Pipe: .000079 ft2
Flow Rate of Fluid: .000237 ft3/s
Absolute Dynamic Viscosity: 1.41x10-5 ft2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION:
Kinematic Viscosity: 1.664x10-5 ft2/s
REYNOLDS NUMBER:
Reynolds Number: 1,802 (LAMINAR FLOW)
vDρ vD (3 ft/s)(.01 ft) Re = = = = 1,802 −5 2 µ υ 1.664x10 ft /s
Area of Pipe: .000079 ft2
Flow Rate of Fluid: .000237 ft3/s
Absolute Dynamic Viscosity: 1.41x10-5 ft2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION:
Kinematic Viscosity: 1.664x10-5 ft2/s
HAGEN-POISEUILLE EQUATION:
Reynolds Number: 1,802 (LAMINAR FLOW)
π R 4 ΔPf π D 4 ΔPf Q= = 8µL 128 µ L
Area of Pipe: .000079 ft2
Flow Rate of Fluid: .000237 ft3/s
Absolute Dynamic Viscosity: 1.41x10-5 ft2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION: HAGEN-POISEUILLE EQUATION:
π R 4 ΔPf π D 4 ΔPf Q= = 8µL 128 µ L
Kinematic Viscosity: 1.664x10-5 ft2/s
FLOW RATE:
Reynolds Number: 1,802 (LAMINAR FLOW)
Area of Pipe: .000079 ft2
Q = Av
Flow Rate of Fluid: .000237 ft3/s
Absolute Dynamic Viscosity: 1.41x10-5 ft2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION: HAGEN-POISEUILLE EQUATION:
π R 4 ΔPf π D 4 ΔPf Q= = 8µL 128 µ L
Kinematic Viscosity: 1.664x10-5 ft2/s
FLOW RATE:
Reynolds Number: 1,802 (LAMINAR FLOW)
Area of Pipe: .000079 ft2
Q = Av AREA:
πd2 A= 4
Flow Rate of Fluid: .000237 ft3/s
Absolute Dynamic Viscosity: 1.41x10-5 ft2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION: HAGEN-POISEUILLE EQUATION:
π R 4 ΔPf π D 4 ΔPf Q= = 8µL 128 µ L
Kinematic Viscosity: 1.664x10-5 ft2/s
Reynolds Number: 1,802 (LAMINAR FLOW)
FLOW RATE:
Area of Pipe: .000079 ft2
Q = Av
Flow Rate of Fluid: .000237 ft3/s
Absolute Dynamic Viscosity: 1.41x10-5 ft2/s
AREA:
πd2 A= 4
π (.01 ft)2 A= 4
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION: HAGEN-POISEUILLE EQUATION:
π R 4 ΔPf π D 4 ΔPf Q= = 8µL 128 µ L
Kinematic Viscosity: 1.664x10-5 ft2/s
Reynolds Number: 1,802 (LAMINAR FLOW)
FLOW RATE:
Area of Pipe: .000079 ft2
Q = Av
Flow Rate of Fluid: .000237 ft3/s
Absolute Dynamic Viscosity: 1.41x10-5 ft2/s
AREA:
πd2 A= 4
π (.01 ft)2 2 A= = .000079 ft 4
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION: HAGEN-POISEUILLE EQUATION:
π R 4 ΔPf π D 4 ΔPf Q= = 8µL 128 µ L
Kinematic Viscosity: 1.664x10-5 ft2/s
Reynolds Number: 1,802 (LAMINAR FLOW)
FLOW RATE:
Area of Pipe: .000079 ft2
Q = Av
Flow Rate of Fluid: .000237 ft3/s
Absolute Dynamic Viscosity: 1.41x10-5 ft2/s
AREA:
πd2 A= 4
π (.01 ft)2 2 A= = .000079 ft 4
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION: HAGEN-POISEUILLE EQUATION:
π R 4 ΔPf π D 4 ΔPf Q= = 8µL 128 µ L
Kinematic Viscosity: 1.664x10-5 ft2/s
Reynolds Number: 1,802 (LAMINAR FLOW)
FLOW RATE:
Area of Pipe: .000079 ft2
Q = Av
Flow Rate of Fluid: .000237 ft3/s
Q = (.000079 ft )(3 ft/s) 2
Absolute Dynamic Viscosity: 1.41x10-5 ft2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION: HAGEN-POISEUILLE EQUATION:
π R 4 ΔPf π D 4 ΔPf Q= = 8µL 128 µ L
Kinematic Viscosity: 1.664x10-5 ft2/s
Reynolds Number: 1,802 (LAMINAR FLOW)
FLOW RATE:
Area of Pipe: .000079 ft2
Q = Av
Flow Rate of Fluid: .000237 ft3/s
Q = (.000079 ft )(3 ft/s) = .000237 ft /s 2
3
Absolute Dynamic Viscosity: 1.41x10-5 ft2/s
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION: HAGEN-POISEUILLE EQUATION:
π R 4 ΔPf π D 4 ΔPf Q= = 8µL 128 µ L
Kinematic Viscosity: 1.664x10-5 ft2/s
Reynolds Number: 1,802 (LAMINAR FLOW)
FLOW RATE:
Area of Pipe: .000079 ft2
Q = Av
Flow Rate of Fluid: .000237 ft3/s
Q = (.000079 ft )(3 ft/s) = .000237 ft /s 2
3
Absolute Dynamic Viscosity: 1.41x10-5 ft2/s
CONSEQUENCES OF FLUID FLOW
CONSEQUENCES OF FLUID FLOW
PROPERTIES OF WATER at various temperatures can be referenced on Page 114 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW
PROPERTIES OF WATER at various temperatures can be referenced on Page 114 of the NCEES Supplied Reference Handbook, version 9.4 for Computer Based Testing
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION:
Kinematic Viscosity: 1.664x10-5 ft2/s
HAGEN-POISEUILLE EQUATION:
Reynolds Number: 1,802 (LAMINAR FLOW)
π R 4 ΔPf π D 4 ΔPf Q= = 8µL 128 µ L
Area of Pipe: .000079 ft2
Flow Rate of Fluid: .000237 ft3/s
Dynamic Viscosity: 3.229x10-5 lbf·s/ft2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION:
Kinematic Viscosity: 1.664x10-5 ft2/s
HAGEN-POISEUILLE EQUATION:
Reynolds Number: 1,802 (LAMINAR FLOW)
π R 4 ΔPf π D 4 ΔPf Q= = 8µL 128 µ L
Area of Pipe: .000079 ft2
Flow Rate of Fluid: .000237 ft3/s
Dynamic Viscosity: 3.229x10-5 lbf·s/ft2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION:
Kinematic Viscosity: 1.664x10-5 ft2/s
HAGEN-POISEUILLE EQUATION:
Reynolds Number: 1,802 (LAMINAR FLOW)
π R 4 ΔPf π D 4 ΔPf Q= = 8µL 128 µ L
Area of Pipe: .000079 ft2
Flow Rate of Fluid: .000237 ft3/s
Dynamic Viscosity: 3.229x10-5 lbf·s/ft2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION:
Kinematic Viscosity: 1.664x10-5 ft2/s
HAGEN-POISEUILLE EQUATION:
Reynolds Number: 1,802 (LAMINAR FLOW)
π D 4 ΔPf Q= 128 µ L
Area of Pipe: .000079 ft2
Flow Rate of Fluid: .000237 ft3/s
Dynamic Viscosity: 3.229x10-5 lbf·s/ft2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION:
Kinematic Viscosity: 1.664x10-5 ft2/s
HAGEN-POISEUILLE EQUATION:
Reynolds Number: 1,802 (LAMINAR FLOW)
4 π (.01 ft) ΔPf 3 .000237 ft /s = -5 2 128(3.229x10 lbf/ft )(30 ft)
Area of Pipe: .000079 ft2
Flow Rate of Fluid: .000237 ft3/s
Dynamic Viscosity: 3.229x10-5 lbf·s/ft2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION:
Kinematic Viscosity: 1.664x10-5 ft2/s
HAGEN-POISEUILLE EQUATION:
Reynolds Number: 1,802 (LAMINAR FLOW)
.000237 ft 3 /s ⎡⎣128(3.229x10 -5 lbf/ft 2 )(30 ft) ⎤⎦ ΔPf = 4 π (.01 ft)
Area of Pipe: .000079 ft2
Flow Rate of Fluid: .000237 ft3/s
Dynamic Viscosity: 3.229x10-5 lbf·s/ft2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION:
Kinematic Viscosity: 1.664x10-5 ft2/s
HAGEN-POISEUILLE EQUATION:
Reynolds Number: 1,802 (LAMINAR FLOW)
.000237 ft 3 /s ⎡⎣128(3.229x10 -5 lbf/ft 2 )(30 ft) ⎤⎦ 2 ΔPf = = 935 lbf/ft 4 π (.01 ft)
Area of Pipe: .000079 ft2
Flow Rate of Fluid: .000237 ft3/s
Dynamic Viscosity: 3.229x10-5 lbf·s/ft2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION:
Kinematic Viscosity: 1.664x10-5 ft2/s
HAGEN-POISEUILLE EQUATION:
Reynolds Number: 1,802 (LAMINAR FLOW)
ΔPf = 935 lbf/ft
2
Area of Pipe: .000079 ft2
Flow Rate of Fluid: .000237 ft3/s
Dynamic Viscosity: 3.229x10-5 lbf·s/ft2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION:
Kinematic Viscosity: 1.664x10-5 ft2/s
HAGEN-POISEUILLE EQUATION:
ΔPf = 935 lbf/ft
2
CONVERSION FROM lbf/ft2 TO lbf/in2:
Reynolds Number: 1,802 (LAMINAR FLOW)
Area of Pipe: .000079 ft2
Flow Rate of Fluid: .000237 ft3/s
Dynamic Viscosity: 3.229x10-5 lbf·s/ft2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION:
Kinematic Viscosity: 1.664x10-5 ft2/s
HAGEN-POISEUILLE EQUATION:
ΔPf = 935 lbf/ft
2
CONVERSION FROM lbf/ft2 TO lbf/in2:
lbf ⎛ 1 ft 2 ⎞ 935 2 ⎜ 2⎟ ft ⎝ 144 in ⎠
Reynolds Number: 1,802 (LAMINAR FLOW)
Area of Pipe: .000079 ft2
Flow Rate of Fluid: .000237 ft3/s
Dynamic Viscosity: 3.229x10-5 lbf·s/ft2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION:
Kinematic Viscosity: 1.664x10-5 ft2/s
HAGEN-POISEUILLE EQUATION:
ΔPf = 935 lbf/ft
2
CONVERSION FROM lbf/ft2 TO lbf/in2:
lbf ⎛ 1 ft 2 ⎞ 2 935 2 ⎜ = 6.49 lbf/in 2⎟ ft ⎝ 144 in ⎠
Reynolds Number: 1,802 (LAMINAR FLOW)
Area of Pipe: .000079 ft2
Flow Rate of Fluid: .000237 ft3/s
Dynamic Viscosity: 3.229x10-5 lbf·s/ft2
CONSEQUENCES OF FLUID FLOW EXAMPLE: Water at 40oF flows from a large reservoir horizontally through a .12 inch diameter stainless steel pipe. If the flow is at a steady at 3 ft/s and the total length of the pipe run is 30 ft, the pressure drop across this section, is most close to: GIVEN:
WATER DISCHARGE ELEVATION = 15 ft
Diameter of Pipe: .01 ft
Velocity in Pipe: 3 ft/s
Temperature of Fluid: 40oF
Length of Pipe: 30 ft
SOLUTION:
Kinematic Viscosity: 1.664x10-5 ft2/s
HAGEN-POISEUILLE EQUATION:
ΔPf = 935 lbf/ft
2
CONVERSION FROM lbf/ft2 TO lbf/in2:
lbf ⎛ 1 ft 2 ⎞ 2 935 2 ⎜ = 6.49 lbf/in 2⎟ ft ⎝ 144 in ⎠
ΔPf = 6.49 psi
Reynolds Number: 1,802 (LAMINAR FLOW)
Area of Pipe: .000079 ft2
Flow Rate of Fluid: .000237 ft3/s
Dynamic Viscosity: 3.229x10-5 lbf·s/ft2
