Uniform Flow Steady Flows AWS
Uniform Flow Steady Flows -
Velocity and flow depth do not change Flow looks the same at all times Steady flow can be uniform, rapidly varying or gradually varying
Unsteady flows -
Flow parameters time dependent Fluid properties vary with time E.g. surge waves
Steady Flows diagram
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Channel bottom – bottom surface of water Water surface – surface of water Energy grade line – Y = flow depth V = water velocity V2/2g = velocity head, difference between water surface and energy H = total head, head from datum to energy grade line (top) H = z + y + v2/2g h = stage, vertical distance from datum to free surface at a point in flow hf = head loss due to friction over a distance L along the channel Sf = slope of energy grade line = hf/L
Open Channel Flow
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A = area P = wetted perimeter Rh = hydraulic radius = A/P Dh = hydraulic diameter = 4A/P
Free Surface vs Closed Conduit Flow
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Hf is head losses Free surface flows more complex – upper boundary, water surface can move vertically, flow area variable
Channel roughness may also be harder to define
Uniform flow -
Ideal and real flows o Ideal flows do not have energy losses due to friction
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o Pressure gradient leads to acceleration of flow o Flow depth decreases o Velocity head increases Real Flows o At a point, friction and gravity are in balance o Uniform flow – flow depth constant o Bed and free surface parallel to energy line
Uniform flow o Flow depth constant in space o Normal flow depth o Bed and free surface parallel Equations o When these forces are balanced, uniform flow
o Assumptions o Τo proportional to v2 o τo = Kρv2
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o o
Chezy
o
o
o o Example
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Graphs for calculating value, use equation if possible
Velocity and flow depth do not change Flow looks the same at all times Steady flow can be uniform, rapidly varying or gradually varying
Unsteady flows -
Flow parameters time dependent Fluid properties vary with time E.g. surge waves
Steady Flows diagram
-
Channel bottom – bottom surface of water Water surface – surface of water Energy grade line – Y = flow depth V = water velocity V2/2g = velocity head, difference between water surface and energy H = total head, head from datum to energy grade line (top) H = z + y + v2/2g h = stage, vertical distance from datum to free surface at a point in flow hf = head loss due to friction over a distance L along the channel Sf = slope of energy grade line = hf/L
Open Channel Flow
-
A = area P = wetted perimeter Rh = hydraulic radius = A/P Dh = hydraulic diameter = 4A/P
Free Surface vs Closed Conduit Flow
-
-
Hf is head losses Free surface flows more complex – upper boundary, water surface can move vertically, flow area variable
Channel roughness may also be harder to define
Uniform flow -
Ideal and real flows o Ideal flows do not have energy losses due to friction
-
-
-
-
o Pressure gradient leads to acceleration of flow o Flow depth decreases o Velocity head increases Real Flows o At a point, friction and gravity are in balance o Uniform flow – flow depth constant o Bed and free surface parallel to energy line
Uniform flow o Flow depth constant in space o Normal flow depth o Bed and free surface parallel Equations o When these forces are balanced, uniform flow
o Assumptions o Τo proportional to v2 o τo = Kρv2
o
o o
Chezy
o
o
o o Example
-
Graphs for calculating value, use equation if possible
