Engineering Thermodynamics
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Steady Flow Energy Equation
(SFEE)
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M=mass flow rate
Q=heat entering control volume
W= work transferred tfrom control volume
c=Velocity of fluid
p=pressure of fluid
u=internal energy/kg of fluid
v=specific volume
h=enthalpy
z2
z1
u1
p1
c1
v1
h1
2
u2
p2
c2
v2
h2
1
DATUM
The Steady-Flow Process
Definition of Steady-Flow Process
A process during which a fluid flows through a
control volume steadily
Characteristics of Steady-Flow Process
1. No properties in the control volume
change with time
2. No properties changes at the
boundaries of the control volume with
time
3. The heat and work interactions between a
steady flow system and its surroundings do not
change with time
Energy Equation of Steady-Flow Process
From the above discussion we can conclude
that:
1.
m  m  m
1
2
2. The net change in energy of CV is Zero
Energy Equation of Steady-Flow
Total energy
crossing
=
boundary per
unit time
Total energy
of mass
leaving CV
per unit time
2
2
Total energy of
mass entering
CV per unit
time
2
1
V
V
Q  W   m2 (h2 
 gz2 )   m1 (h1 
 gz1 )
2
2
V12
V22
Q  W   m1 (h1 
 gz1 )   m2 (h2 
 gz2 )  0
2
2
since
 m  m
2
1
m
V22
V12
Q  W  m(h2 
 gz2 )  m(h1 
 gz1 )
2
2
Using subscript 1and subscript 2 for denoting inlet
and exit states
V22  V12
Q  W  m[h2  h1 
 g ( z2  z1 )]
2
Dividing the equation by m yields
V V
q  w  h2  h1 
 g ( z2  z1 )
2
2
2
2
1
V
q  h 
 gz  w
2
2
or
2


V
q  u   pv 
 gz  w 
2


Work
Some Steady-Flow Engineering devices
For Nozzle,
Nozzles
(1) No work input/output,
W=0
IN
1
2
(2) No heat interaction,
OUT
Q=0
(3) z1-z2=0
Hence c1 2 -c2 2
c2= 2(h1-h2)
For Diffuser,
Diffuser
(1) No work input/output,
W=0
1
IN
2
(2) No heat interaction,
OUT
Q=0
(3) z1-z2=0
Hence c2 2 -c1 2
c1= 2(h2-h1)
c1= 2Cp(T2-T1)
Boiler
For Boiler,
(1) No work input/output, W=0
(2) Change of kinetic energy is
negligible, c1=c2
Heat
Combustion of fuel
(3) z1-z2=0
Hence mh1+Q = mh2
Q = m(h2-h1)
Steam Turbine
For Steam/Gas turbine,
2
(1) z1=z2
(2) c1=c2
Turbine
Generator
(3) Q=0
(4) W=0
1
Hence mh1=mh2+W
W=m(h1-h2)
Throttling Device
(1)Q=0
(2)W =0
(3)z =0
(4)Δc=0
Then,
Δh =0
That is
h1 = h 2
Heat exchangers
It is a device which transfer
heat from one fluid to another
Some examples of
Heat exchangers are
(1) Condenser
(2) Evaporator
(3) Automobile Radiator
Condenser
For Steam/Gas turbine,
1
(1) z1=z2
2’ (2) c1=c2
1’
(3) W=0
2
Hence mh1+Q=mh2
Q=m(h2-h1)
Evaporator
For Steam/Gas turbine,
(1) z1=z2
1
2
(2) c1=c2
(3) W=0 (No shaft work)
Hence mh1+Q=mh2
Q=m(h2-h1)
Automobile Radiator
For Steam/Gas turbine,
(1) z1 =z2
(2) c1 =c2
(3) W =0
(4) Q= -Q , heat lost by water
Hence mh2+Q=mh1
Q=m(h1-h2)
=mCp(T1-T2)