Ch. 4 The first law of
thermodynamics:
Control Volume
4.1 Thermodynamic analysis of
control volumes
 Control Volume
 Control Surface
 Steady: No change with time
 Unsteady, Transient
 Uniform: No change with location
Thermodynamic analysis of control
volumes
 Conservation of Mass Principle
Total
mass entering
CV
Total
-
mass leaving
Net change
=
CV
In mass within
CV
 Mass and Volume Flow Rates
Mass Flow Rate: Amount of mass flowing through a
cross section per unit time
Mass Flow Rate
 It is proportional to the cross-sectional area A, the
density , the velocity V of the fluid.
&
m   Vn dA
A
Vn: Velocity component normal to dA
&
m  Vav dA
Vav : Average fluid velocity normal to A
Volume Flow Rate
 Volume of the fluid flowing through a cross-
section per unit time
V   Vn dA  Vav A
A
 The mass and volume flow rate:
m  V  V
v
Conservation of Energy Principle
 In closed system
Net heat(Q) – Work(W) = Energy change(E)
 When mass enters or leaves a control volume,
the energy increase or decrease within the
control volume.
Conservation of Energy Principle
The conservation of energy equation for a control volume
 Total energy

 Total energy   Total energy   Net change 



 
 

crossing
boundary

of
mass

of
mass

in
energy



 
 

 as heat and work 
 entering CV   leaving CV   of CV




 
 

Q  W   Ein , mass   Eout , mass  ECV
The energy required ot push fluid into or out of a control
volume is called the flow work, or flow energy.
Flow Work
 If the fluid pressure is P and the cross-sectional area
of the fluid element A, the force applied on the fluid
element by the imaginary piston F = PA.
 The work done in pushing the fluid element
Wflow = FL = PAL =PV
Total Energy of a Flowing Fluid
 Three Parts of total energy of a simple compressible
system: Internal, Kinetic, and Potential energies.
 On a unit mass basis,
V2
e  u  ke  pe  u 
 gz
2
 Total energy of a flowing fluid on a unit mass basis ()
  Pv  e  Pv  u  ke  pe 
Total Energy of a Flowing Fluid
 By the definition of enthalpy (h = u + Pv):
V2
  h  ke  pe  h 
 gz
2
 : Methalphy Metaenthalpy, which means beyond
enthalphy
Steady Flow Process
 Process during which a fluid flows through a
control volume steadily
 Steady flow devices: Turbines, compressors,
and nozzles operating for long periods of time
under the same conditions
 Steady means no change with time.
Steady Flow Process
No properties (volume, mass, total energy) within
the control volume change with time. The boundary
work is zero for steady flow systems since Vcv is
constant.
2. No properties change at the boundaries of the
control volume with time. The mass flow rate of the
fluid at an opening must remain constant during a
steady flow process.
3. The heat and work interactions between a steady
flow system and its surrounding do not change with
time
1.
Conservation of Mass
 During a steady flow process, the total
amount of mass in CV does not change with
time. (Entering Mass = Leaving Mass)
 Total mass 
 Total mass 




 entering CV    leaving CV 
 per unit time 
 per unit time 




Conservation of Energy
Water Heater under steady operation:
 The water stream will experience an increase in its
total energy as it flows through the water heater,
which is equal to the electric energy supplied to the
water minus the heat losses.
Conservation of Energy
 Total energy
  Total energy
  Total energy 

 
 

crossing
boundary
transported
out
of
transported
into


 

 as heat and work   CV with mass
  CV with mass 

 
 

per
unit
time
per
unit
time
per
unit
time

 
 

Q  W   me  e   mi  i
 = h + ke + pe




Ve2
Vi 2
Q  W   me  he 
 gze    mi  hi 
 gzi 
2
2




for each exit
for each inlet
Single-Stream Steady-Flow Systems
 One inlet and one exit
 Mass flow rate through the entire CV remains
constant


V12  V22
Q  W  m  ( h1  h2 ) 
 g ( z1  z 2 )  ( kW )
2


Q  W  m  h  ke  pe  (kW )
For unit-mass basis
V12  V22
q  w  (h1  h2 ) 
 g ( z1  z2 ) (kW / kg )
2
q  w  m  h  ke  pe  (kW / kg )
Single-Stream Steady-Flow Systems
 If
ke  0, pe  0
Then q  w  h ( kJ / kg )
Q Rate of heat transfer b/w CV and its surroundings
W = Power (work done per unit time)
h  hexit  hinlet
ke  V22  V12  / 2
pe  g  z 2  z1 
Some Steady-Flow Engineering Device
 Nozzles and Diffusers
Jet engines, rockets, spacecraft, garden hoses
Nozzle: Device to increase the velocity of a fluid
Diffuser: Device to increase the pressure of a fluid by
slowing it down.
Q0
W 0
ke  0
pe  0
Some Steady-Flow Engineering Device
 Turbines
Steam, gas, hydroelectric power plants
As the fluid passes through the turbine, work is done
against the blades which are attached to the shaft.
 Compressors
Device to increase the pressure of a fluid
Q0
W 0
ke  0
pe  0
Some Steady-Flow Engineering Device
 Throttling Valves
Adjustable valves, capillary tubes, porous plugs
Any kind of flow-restricting devices that cause a
significant pressure drop in the fluid.
Some Steady-Flow Engineering Device
 Heat Exchangers
Devices to exchange heat with mixing of two moving fluid
streams.
Double-tube (tube and shell) heat exchanger
Some Steady-Flow Engineering Device
 Pipe and Duct Flow
Transport of liquids or gases
Flow through a pipe or a duct usually satisfies the steady flow
conditions except the transient start-up and shut-down periods