Open Systems
Law of Conservation of Mass
Thermodynamic Systems • Open system (control volume): a fixed region in space
• Mass can be neither created nor destroyed • “Everything has to go somewhere”
Mass flow out Accumulation Decay Mass flow in
Law of Conservation of Mass • Mass can be neither created nor destroyed • “Everything has to go somewhere”
Law of Conservation of Mass • At the inlet, for an average flow velocity, the mass flowrate is v = flow velocity •
m=ρ v A
Accumulation: flowrate from tap > flowrate through drain
•
→ Sink fills up
m=
1
υ
vA
Decay: (start with a full sink) flowrate from tap < flowrate through drain
•
V=
→ Sink empties
Law of Conservation of Mass • Mass balance:
•
m
ρ
=vA
Volumetric flowrate
Law of Conservation of Mass • Steady flow process
⎧Total mass⎫ ⎧Total mass⎫ ⎧ Net change of mass⎫ ⎬ ⎬=⎨ ⎬−⎨ ⎨ ⎩ entering ⎭ ⎩ leaving ⎭ ⎩ in the system ⎭
⎧Total mass⎫ ⎧Total mass⎫ ⎨ ⎬=⎨ ⎬ ⎩ entering ⎭ ⎩ leaving ⎭
•
•
m in − m out =
Δmsystem Δt •
•
•
m in − m out =
Δmsystem
•
Δt
For a system with multiple inlets and outlets
•
m in − m out =
•
•
Σm in − Σ m out =
m in = m out
dmsystem mcv constant
dt
No Accumulation
dmsystem dt
•
=0
Mass flow in
No Decay
Mass flow out
Law of Conservation of Mass • Steady flow process
• Steady flow process
– Mass and energy contents of control volume remain constant
Law of Conservation of Mass • Steady flow process
– Fluid properties at inlets and outlets remain constant
Energy Transfer in Closed Systems • Energy transfer between a closed system and the surroundings is accomplished by:
– Incompressible flow •
Law of Conservation of Mass
•
m in = m out
– Exchanging heat – Performing work
•
m=ρ v A
ρ in v in Ain = ρ out v out Aout since
ρ in = ρ out
v in Ain = v out Aout
Energy Transfer in Open Systems • Energy transfer between an open system and the surroundings is accomplished by:
Energy Balance for Steady Flow Systems • Total energy of a nonflowing fluid:
e = u + ke + pe = u +
– Exchanging heat – Performing work – Mass flow
v2 + gz 2
• Total energy of a flowing fluid: Flow energy
θ = Pυ + u + ke + pe Enthalpy
ΔEsystem = (Qin − Qout ) + (Win − Wout ) + ( Emass ,in − Emass ,out )
θ = h + ke + pe = h +
v2 + gz 2
Energy Balance for Steady Flow Systems
Energy Balance for Steady Flow Systems
• Flow work: the energy needed to push a fluid into or out of a control volume
• Flow work: the energy needed to push a fluid into or out of a control volume
First Law
First Law for Open Systems For multiple inlets and outlets:
• Closed systems
•
Qin − Wout = ΔU + ΔKE + ΔPE
•
•
•
Qin − Wout = Σ [ mout ( hout + keout + peout )] − Σ [min (hin + kein + pein )]
For steady flow system with a single stream:
Qin − Wout = m(u2 + ke2 + pe2 ) − m(u1 + ke1 + pe1 )
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•
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•
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•
• Open systems •
•
•
•
•
•
•
•
•
•
Qin − Wout = m(hout − hin ) +
•
qin − wout = ( hout − hin ) +
Qin − Wout = ΔH + ΔKE + ΔPE Qin − Wout = mout (hout + keout + peout ) − min (hin + kein + pein )
Applications of First Law for Open Systems
•
Qin − Wout = m(hout − hin ) + m(keout − kein ) + m( peout − pein ) •
m mg 2 2 ( v out − v in ) + ( zout − zin ) 2gc gc
1 g 2 2 ( v out − v in ) + ( zout − zin ) 2 gc gc
Bernoulli Principle
Nozzles and Diffusers
“As the speed of a moving fluid increases, the pressure within the fluid decreases.”
• Nozzle: increases the velocity of a fluid at the expense of pressure • Diffuser: increases the pressure of a fluid by slowing it down Daniel Bernoulli (1700-1782)
Bernoulli Equation
Bernoulli Equation
P = static pressure
Bernoulli Principle • Static Pressure: – Actual thermodynamic pressure of the fluid – Pressure felt by an object not moving relative to the fluid (i.e., suspended in the fluid and moving with it) – Static pressure decreases when velocity increases
Applications of First Law for Open Systems
Bernoulli Principle • Ram Pressure: – Pressure felt by an object moving relative to the fluid – Ram pressure increases when velocity increases
Applications of First Law for Open Systems •
Nozzles and Diffusers
•
•
•
•
Qin − Wout = ΔH + ΔKE + ΔPE Nozzles and Diffusers • High velocities → short residence times • Insignificant heat transfer, no work, no change in potential energy •
•
0 = ΔH + ΔKE (hout − hin ) =
1 2 2 ( v in − v out ) 2 gc
Applications of First Law for Open Systems Turbines and Compressors
Applications of First Law for Open Systems Turbines
• Turbine: produces work as fluid passes through, spins blades, and turns shaft – Work done by fluid – Produces power output
• Compressor / pump / fan: increases the pressure of a fluid – Work supplied by external source
COMPRESSOR
Axial flow turbine
– Requires power input
Hydraulic turbine
Applications of First Law for Open Systems
Applications of First Law for Open Systems •
•
•
•
•
Qin − Wout = ΔH + ΔKE + ΔPE
Turbines Hydraulic turbine
Turbines
Steam turbine
• Heat transfer usually negligible (insulated), no change in potential energy •
•
•
− Wout = ΔH + ΔKE •
wout = (hin − hout ) +
1 2 2 ( v in − v out ) 2gc
•
wout = (hin − hout )
Applications of First Law for Open Systems Compressors
Reciprocating compressor
Applications of First Law for Open Systems Compressors
Axial-flow compressor
Centrifugal compressor
Reciprocating compressor
Axial-flow compressor
Applications of First Law for Open Systems •
•
•
•
•
Qin − Wout = ΔH + ΔKE + ΔPE Compressors • May or may not be insulated, no change in potential energy •
•
•
Applications of First Law for Open Systems Throttling Valves • Flow-restricting devices that cause a significant pressure drop
•
Qin − Wout = ΔH + ΔKE •
•
qin − wout = (hout − hin ) +
1 2 2 ( v out − v in ) 2 gc
Applications of First Law for Open Systems •
•
•
•
Qin − Wout = ΔH + ΔKE + ΔPE Throttling Valves • Negligible heat transfer (short residence times) • No mechanical work involved • Negligible change in velocity of the fluid / no change in potential energy •
ΔH = 0
Internal energy + Flow energy = constant
hout = hin u1 + Pυ1 = u2 + Pυ 2
Applications of First Law for Open Systems •
•
•
•
•
Qin − Wout = ΔH + ΔKE + ΔPE Heat Exchangers • No mechanical work involved • Negligible change in kinetic and potential energies •
•
Qin = ΔH •
qin = (hout − hin ) •
qout = (hin − hout )
Applications of First Law for Open Systems
•
Heat Exchangers • Two moving streams of fluid exchange heat without mixing
Thermodynamic Systems • Open system (control volume): a fixed region in space
• Mass can be neither created nor destroyed • “Everything has to go somewhere”
Mass flow out Accumulation Decay Mass flow in
Law of Conservation of Mass • Mass can be neither created nor destroyed • “Everything has to go somewhere”
Law of Conservation of Mass • At the inlet, for an average flow velocity, the mass flowrate is v = flow velocity •
m=ρ v A
Accumulation: flowrate from tap > flowrate through drain
•
→ Sink fills up
m=
1
υ
vA
Decay: (start with a full sink) flowrate from tap < flowrate through drain
•
V=
→ Sink empties
Law of Conservation of Mass • Mass balance:
•
m
ρ
=vA
Volumetric flowrate
Law of Conservation of Mass • Steady flow process
⎧Total mass⎫ ⎧Total mass⎫ ⎧ Net change of mass⎫ ⎬ ⎬=⎨ ⎬−⎨ ⎨ ⎩ entering ⎭ ⎩ leaving ⎭ ⎩ in the system ⎭
⎧Total mass⎫ ⎧Total mass⎫ ⎨ ⎬=⎨ ⎬ ⎩ entering ⎭ ⎩ leaving ⎭
•
•
m in − m out =
Δmsystem Δt •
•
•
m in − m out =
Δmsystem
•
Δt
For a system with multiple inlets and outlets
•
m in − m out =
•
•
Σm in − Σ m out =
m in = m out
dmsystem mcv constant
dt
No Accumulation
dmsystem dt
•
=0
Mass flow in
No Decay
Mass flow out
Law of Conservation of Mass • Steady flow process
• Steady flow process
– Mass and energy contents of control volume remain constant
Law of Conservation of Mass • Steady flow process
– Fluid properties at inlets and outlets remain constant
Energy Transfer in Closed Systems • Energy transfer between a closed system and the surroundings is accomplished by:
– Incompressible flow •
Law of Conservation of Mass
•
m in = m out
– Exchanging heat – Performing work
•
m=ρ v A
ρ in v in Ain = ρ out v out Aout since
ρ in = ρ out
v in Ain = v out Aout
Energy Transfer in Open Systems • Energy transfer between an open system and the surroundings is accomplished by:
Energy Balance for Steady Flow Systems • Total energy of a nonflowing fluid:
e = u + ke + pe = u +
– Exchanging heat – Performing work – Mass flow
v2 + gz 2
• Total energy of a flowing fluid: Flow energy
θ = Pυ + u + ke + pe Enthalpy
ΔEsystem = (Qin − Qout ) + (Win − Wout ) + ( Emass ,in − Emass ,out )
θ = h + ke + pe = h +
v2 + gz 2
Energy Balance for Steady Flow Systems
Energy Balance for Steady Flow Systems
• Flow work: the energy needed to push a fluid into or out of a control volume
• Flow work: the energy needed to push a fluid into or out of a control volume
First Law
First Law for Open Systems For multiple inlets and outlets:
• Closed systems
•
Qin − Wout = ΔU + ΔKE + ΔPE
•
•
•
Qin − Wout = Σ [ mout ( hout + keout + peout )] − Σ [min (hin + kein + pein )]
For steady flow system with a single stream:
Qin − Wout = m(u2 + ke2 + pe2 ) − m(u1 + ke1 + pe1 )
•
•
•
•
•
•
• Open systems •
•
•
•
•
•
•
•
•
•
Qin − Wout = m(hout − hin ) +
•
qin − wout = ( hout − hin ) +
Qin − Wout = ΔH + ΔKE + ΔPE Qin − Wout = mout (hout + keout + peout ) − min (hin + kein + pein )
Applications of First Law for Open Systems
•
Qin − Wout = m(hout − hin ) + m(keout − kein ) + m( peout − pein ) •
m mg 2 2 ( v out − v in ) + ( zout − zin ) 2gc gc
1 g 2 2 ( v out − v in ) + ( zout − zin ) 2 gc gc
Bernoulli Principle
Nozzles and Diffusers
“As the speed of a moving fluid increases, the pressure within the fluid decreases.”
• Nozzle: increases the velocity of a fluid at the expense of pressure • Diffuser: increases the pressure of a fluid by slowing it down Daniel Bernoulli (1700-1782)
Bernoulli Equation
Bernoulli Equation
P = static pressure
Bernoulli Principle • Static Pressure: – Actual thermodynamic pressure of the fluid – Pressure felt by an object not moving relative to the fluid (i.e., suspended in the fluid and moving with it) – Static pressure decreases when velocity increases
Applications of First Law for Open Systems
Bernoulli Principle • Ram Pressure: – Pressure felt by an object moving relative to the fluid – Ram pressure increases when velocity increases
Applications of First Law for Open Systems •
Nozzles and Diffusers
•
•
•
•
Qin − Wout = ΔH + ΔKE + ΔPE Nozzles and Diffusers • High velocities → short residence times • Insignificant heat transfer, no work, no change in potential energy •
•
0 = ΔH + ΔKE (hout − hin ) =
1 2 2 ( v in − v out ) 2 gc
Applications of First Law for Open Systems Turbines and Compressors
Applications of First Law for Open Systems Turbines
• Turbine: produces work as fluid passes through, spins blades, and turns shaft – Work done by fluid – Produces power output
• Compressor / pump / fan: increases the pressure of a fluid – Work supplied by external source
COMPRESSOR
Axial flow turbine
– Requires power input
Hydraulic turbine
Applications of First Law for Open Systems
Applications of First Law for Open Systems •
•
•
•
•
Qin − Wout = ΔH + ΔKE + ΔPE
Turbines Hydraulic turbine
Turbines
Steam turbine
• Heat transfer usually negligible (insulated), no change in potential energy •
•
•
− Wout = ΔH + ΔKE •
wout = (hin − hout ) +
1 2 2 ( v in − v out ) 2gc
•
wout = (hin − hout )
Applications of First Law for Open Systems Compressors
Reciprocating compressor
Applications of First Law for Open Systems Compressors
Axial-flow compressor
Centrifugal compressor
Reciprocating compressor
Axial-flow compressor
Applications of First Law for Open Systems •
•
•
•
•
Qin − Wout = ΔH + ΔKE + ΔPE Compressors • May or may not be insulated, no change in potential energy •
•
•
Applications of First Law for Open Systems Throttling Valves • Flow-restricting devices that cause a significant pressure drop
•
Qin − Wout = ΔH + ΔKE •
•
qin − wout = (hout − hin ) +
1 2 2 ( v out − v in ) 2 gc
Applications of First Law for Open Systems •
•
•
•
Qin − Wout = ΔH + ΔKE + ΔPE Throttling Valves • Negligible heat transfer (short residence times) • No mechanical work involved • Negligible change in velocity of the fluid / no change in potential energy •
ΔH = 0
Internal energy + Flow energy = constant
hout = hin u1 + Pυ1 = u2 + Pυ 2
Applications of First Law for Open Systems •
•
•
•
•
Qin − Wout = ΔH + ΔKE + ΔPE Heat Exchangers • No mechanical work involved • Negligible change in kinetic and potential energies •
•
Qin = ΔH •
qin = (hout − hin ) •
qout = (hin − hout )
Applications of First Law for Open Systems
•
Heat Exchangers • Two moving streams of fluid exchange heat without mixing
