Week 8. Steady Flow
Engineering Devices
GENESYS Laboratory
Objectives
1.
2.
Solve energy balance problems for common steady-flow devices such as
nozzles, compressors, turbines, throttling valves, mixers, heaters, and
heat exchangers
Apply the energy balance to general unsteady-flow processes with
particular emphasis on the uniform-flow process as the model for
commonly encountered charging and discharging processes
GENESYS Laboratory
Some Steady-Flow Engineering Devices
• The components of a steam plant (Turbines, compressors, heat exchanger, and pumps)
can be conveniently analyzed as steady-flow devices.
GENESYS Laboratory
Nozzles and Diffusers
• Nozzle: a device that increases the velocity of a fluid at the expense of pressure
• Diffuser : a device that increases the pressure of a fluid by slowing it down
2
2


V
−
V
1
Qɺ − Wɺ = mɺ  h2 − h1 + 2
+ g ( z2 − z1 ) 
2


Assumptions
Qɺ ≈ 0 (the fluid has high velocity)
Wɺ = 0
∆pe ≅ 0
V22 − V12
h1 − h2 =
2
Subsonic flows
GENESYS Laboratory
Ex1) Deceleration of Air in a Diffuser
GENESYS Laboratory
Ex2) Acceleration of Steam in a Nozzle
GENESYS Laboratory
Turbines and Compressors
• Turbine: a device that drives the electric generator
• Compressor: a device that increases the pressure of a fluid
2
2


V
V
−
2
1
Qɺ − Wɺ = mɺ  h2 − h1 +
+ g ( z2 − z1 ) 
2


Assumptions
Qɺ ≈ 0 (well insulated)
∆pe ≅ 0
∆ke ≅ 0 ← ∆ke⟨⟨∆h
Wɺ = mɺ ( h1 − h2 )
GENESYS Laboratory
Compressor
During the same t
GENESYS Laboratory
Ex3) Compressing Air by a Compressor
GENESYS Laboratory
Ex4) Power Generation by a Steam Turbine
GENESYS Laboratory
Throttling Valves
• Throttling valve: a device that cause large pressure drops in the fluid
2
2


V
−
V
2
1
ɺ
ɺ
+ g ( z2 − z1 ) 
Q − W = mɺ  h2 − h1 +
2


Assumptions
Qɺ ≈ 0 (well insulated)
Wɺ ≈ 0
∆pe ≅ 0
∆ke ≅ 0 ← ∆ke⟨⟨∆h
h2 ≅ h1 ← isenthalpic device or constant enthalpy device
⇒ u1 + Pv
1 1 = u2 + P2 v2
GENESYS Laboratory
Ex5) Expansion of Refrigerant-134a in a Refrigerator
GENESYS Laboratory
Mixing Chambers
• Mixing chamber: a section where the mixing process takes place
2
2


V
−
V
2
1
ɺ
ɺ
Q − W = mɺ  h2 − h1 +
+ g ( z2 − z1 ) 
2


Assumptions
Qɺ ≈ 0 (well insulated)
Wɺ = 0
∆pe ≅ 0
∆ke ≅ 0
mɺ ( h1 − h2 ) = 0
GENESYS Laboratory
Ex6) Mixing of Hot and Cold Waters in a Shower
60˚C
150 kPa
10˚C
45˚C
GENESYS Laboratory
Heat Exchangers
• Heat exchanger: a device where two moving fluid streams exchange heat without mixing
2
2


−
V
V
2
1
ɺ
ɺ
Q − W = mɺ  h2 − h1 +
+ g ( z2 − z1 ) 
2


Assumptions
Qɺ → depending on the control volume
Wɺ = 0
∆pe ≅ 0
∆ke ≅ 0
mɺ ( h1 − h2 ) = 0
mɺ ( h − h ) = Qɺ
2
1
GENESYS Laboratory
Ex7) Cooling of Refrigerant-134a by Water
GENESYS Laboratory
Pipe and Duct Flow
2
2


V
−
V
2
1
Qɺ − Wɺ = mɺ  h2 − h1 +
+ g ( z2 − z1 ) 
2


Assumptions
Qɺ → depending on the control volume
Wɺ → depending on the control volume
∆pe ≅ 0
∆ke ≅ 0
Qɺ cv − Wɺcv = mɺ ( h2 − h1 )
at incompressible substance
∆h = h2 − h1 = ( u 2 −u1 ) + v ( P2 − P1 )
= c(T2 − T1 ) + v ( P2 − P1 )
GENESYS Laboratory
Ex8) Electric Heating of Air in a House
GENESYS Laboratory
Energy Analysis of Unsteady-Flow Processes
• Unsteady-flow : processes involving changes within the control volume with time
• The shape and size of a control volume may change during an unsteady-flow process
• Uniform flow process: the fluid flow at any inlet or exit is uniform and steady, and
thus the fluid properties do not change with time or position over the cross section
of an inlet or exit. If they do, they are averaged and treated as constants for the
entire process.
GENESYS Laboratory
Energy Analysis of Unsteady-Flow Processes II
• Energy balance for a uniform-flow system


 
+
+
θ
−
+
+
θ
Q
W
m
Q
W
m
∑
∑
in
out
 = ( m2 e2 − m1e1 )system
 in
  out

in
 
out

where, θ = h + ke + pe
e = u + ke + pe
If ∆KE ≅ 0, ∆PE ≅ 0
Q − W = ∑ mh −∑ mh + ( m2u2 − m1u1 )system
out
in
Q = Qnet,in = Qin − Qout
W = Wnet,out = Wout − Win
• Although both the steady-flow and uniform-flow processes are somewhat
idealized, many actual processes can be approximated reasonably well by one of
these with satisfactory results
GENESYS Laboratory
Summary
An universal form of Energy balance equation
desystem
ein − eout =
=0
dt
mass balance
mi − me = (m2 − m1 )CV
for a general steady-flow system


 
 Qin + Win + ∑ mθ  −  Qout + Wout + ∑ mθ  = 0

in
 
out

for a general unsteady-flow system


 
Q
+
W
+
m
θ
−
Q
+
W
+
m
θ
∑
∑
in
out
 = ( m2 e2 − m1e1 )system
 in
  out

in
 
out

where, θ = h + ke + pe
e = u + ke + pe
GENESYS Laboratory
Ex9) Charging of a Rigid Tank by Steam
GENESYS Laboratory
Ex10) Cooking with a Pressure Cooker
GENESYS Laboratory