First Law of Thermodynamics FOR
OPEN SYSTEMS
Inserting expression for flow work
 W flow 

pv m 
outlets

pv m
inlets
and regrouping terms
dE C V 
  m (u 
pv  v / 2  gz )
2
inlets


 m ( u  pv  v / 2  gz )   Q   W C V
2
outlets
For rate processes dividing both sides by t and
letting t0
dE C V

dt

m ( h  V / 2  gz ) 
2
inlets

m (h  V
2
Recall enthalpy
defn.:
h=u+pv
/ 2  g z )  Q net , in  W C V
ou tl e ts
For large processes provided all inlet/outlet conditions are
steady (not changing with time) integrate both sides
 ECV 

inlets
m ( h  V / 2  gz ) 
2

out lets
m ( h  V / 2  gz )  Q net , in  W C V
2
The steady flow process
•
•
•
A process during which the fluid flows steadily through the control volume (CV)
– Flow process fluid flows through CV.
– Steady not changing with time
During a steady flow process:
– conditions (fluid properties, flow velocity, elevation) at any fixed point within the CV are
unchanging with time.
– Properties, flow velocity or elevation may change from point to point within CV
– Size, shape, mass and energy content of the CV do not change with time.
– Rate at which heat and work interactions take place with surroundings do not change with
time.
Devices/systems which undergo steady flow process: compressors, pumps, turbines, water supply
pipes, nozzles, heat exchangers, power plants, aircraft engines etc.
Conservation of mass and energy for a
steady flow process
dm C V

dt
dE C V
dt
.
 Q  WCV 

m
m (h 
V
 m (h 
V

2
 gz ) 
2
 m (h 
V
out
m
2
 gz )
2
Conservation of mass
inlets
2
2
m
outlets
in
outlets
outlets
m
inlet s



.
 gz )  Q  W C V 

inlets
m (h 
V
2
 gz )
2
Conservation of energy
Conservation of mass for the steady flow
process
• Mass balance for steady flow

inlets
m

m
outlets
• Assuming uniform 1D flow at each inlet/outlet
m 
AV
v
• A single stream (single inlet-single outlet) control volume
m1  m 2 
1
2
A1V1
v1

A2V 2
v2
Applications of SFEE
• Nozzles and diffusers (e.g. jet propulsion)
• Turbines (e.g. power plant, turbofan/turbojet aircraft
engine), compressors and pumps (power plant)
• Heat exchangers (e.g. boilers and condensers in power
plants, evaporator and condenser in refrigeration, food and
chemical processing)
• Mixing chambers (power plants)
• Throttling devices (e.g. refrigeration, steam quality
measurement in power plants)
All elements of a simple power plant/ refrigeration cycle
and more! In principle, you can take the elements together
to calculate power generated/required, heat
removed/supplied.
Applications of SFEE in pictures
Heat exchangers
Source: internet
Throttling devices
SFEE applied to nozzles/diffusers

m (h 
V
2
2
outlets
.
 gz )  Q  W C V 

inlets
Single stream
hout 
V out
2
2
 hin 
V in
2
2
m (h 
V
2
2
 gz )
SFEE applied to turbines
m ( hout  hin 
V
2
out
2
Usually
)  Q  W cv
V out  V in
2
hout  hin  
V
2
in
2
2
m ( hout  hin )   Q
W c v  m ( hi n  hou t )  0
Enthalpy changes and kinetic energy:
typical magnitudes
• For example, saturated steam at 100 kPa is
flowing through a pipe. The steam is supplied
heat at constant pressure to raise its
temperature to 1500C. What is the ratio of
kinetic energy per unit mass of the steam to
the specific enthalpy change of the steam if
steam is flowing at 100 m/s?
Ans. (100)^2/(2776.6-2675.6)/2000=5%
In steady flow devices like turbines, compressors/pumps, heat exchangers,
throttling devices it is usually a good approximation to neglect flow kinetic energy
(or kinetic energy changes). Exception: nozzles and diffusers.
SFEE applied to compressors
m ( hout  hin 
V
Usually
V
2
2
in
)  Q  W cv
V out  V in
2
hout  hin  
2
out
2
2
m ( hout  hin )   Q
W cv   m ( hout  hin )  0
SFEE for liquid nozzles, pumps and water turbine:
toward the Bernoulli equation
m ( ho u t  hin 
V
2
out
V
2
in
2
 g ( z out  z in ))  Q  W c v
Further assumptions:
A. Incompressible substance,
B. Negligible heat transfer
C. negligible friction despite “the rubbing liquid layers”
D. B and C leading to near isothermal operation.
hout  hi n  v ( p o ut  p in )
W cv
2
2

 V out

 V in
  m  v ( p out  p in )  
 g ( z out  z in )  
2



2
2
 p o u t V out

p in V in
  m (

 g z out )  (

 g z in ) 
2

2
 

SFEE applied to heat exchangers
hot (h)
cold (c)
m c hc , out  m h hh , out  m c hc ,in  m h hh ,in
Take CV enclosing the stream that
is hot at inlet
m h ( h h , o u t  h h , in )   Q
Take CV enclosing the stream that
is cold at inlet
m c ( h c , o u t  hc , in )  Q
Mixing chambers or “direct contact
heat exchangers”
3
2
1
m 3  m1  m 2
Conservation of mass
m 1 h1  m 2 h 2   m 1  m 2  h3
Conservation of energy