where euV^2 /2 gzis the total energy per unit mass for both the con-

trol volume and flow streams. Then,

(5–58)

or

(5–59)

where we used the definition of enthalpy huPvuP/r. The last

two equations are fairly general expressions of conservation of energy, but

their use is still limited to uniform flow at inlets and outlets and negligible

work due to viscous forces and other effects. Also, the subscript “net,in” stands

for “net input,” and thus any heat or work transfer is positive if tothe system

and negative if fromthe system.

a

in

m#ah

V^2

2

gzb

Q

#

net,in
W

#

shaft,net out

d

dt

(^)

CV
er¬dVa
out
m

ah
V^2
2
gzb

a
in
m#a
P
r
u
V^2
2
gzb
Q

net,in
W

shaft,net out
d
dt
(^)

CV
er¬dVa
out
m

a
P
r
u
V^2
2
gzb
Chapter 5 | 255
The conservation of mass principlestates that the net mass
transfer to or from a system during a process is equal to the
net change (increase or decrease) in the total mass of the sys-
tem during that process, and is expressed as
where msystemmfinal
minitialis the change in the mass of
the system during the process,m.inand m.outare the total rates
of mass flow into and out of the system, and dmsystem/dtis the
rate of change of mass within the system boundaries. The
relations above are also referred to as the mass balanceand
are applicable to any system undergoing any kind of process.
The amount of mass flowing through a cross section per
unit time is called the mass flow rate, and is expressed as
where rdensity of fluid,Vaverage fluid velocity nor-
mal to A, and Across-sectional area normal to flow direc-
tion. The volume of the fluid flowing through a cross section
per unit time is called the volume flow rateand is expressed as
The work required to push a unit mass of fluid into or out
of a control volume is called flow workor flow energy, and is
expressed as wflowPv. In the analysis of control volumes,
it is convenient to combine the flow energy and internal
V

VAm

r
m# rVA
min
mout¢msystem¬and¬m

in
m

outdmsystem>dt
energy into enthalpy. Then the total energy of a flowing fluid
is expressed as
The total energy transported by a flowing fluid of mass m
with uniform properties is mu. The rate of energy transport
by a fluid with a mass flow rate of m.is m.u. When the kinetic
and potential energies of a fluid stream are negligible, the
amount and rate of energy transport become Emassmhand
E
.
massm
.h, respectively.
The first law of thermodynamicsis essentially an expres-
sion of the conservation of energy principle, also called the
energy balance.The general mass and energy balances for
any systemundergoing any processcan be expressed as
Net energy transfer Changes in internal, kinetic,
by heat, work, and mass potential, etc., energies
It can also be expressed in the rate formas
Rate of net energy transfer Rate of change in internal, kinetic,
by heat, work, and mass potential, etc., energies
Thermodynamic processes involving control volumes can
be considered in two groups: steady-flow processes and
E

in
E

out^ ^ dEsystem>dt
Ein
Eout  ¢Esystem
uhkepeh
V^2
2
gz
SUMMARY
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