51
Chapter 5
MASS AND ENERGY ANALYSIS OF CONTROL
VOLUMES
Conservation of Mass
51C
Mass, energy, momentum, and electric charge are conserved, and volume and entropy are not
conserved during a process.
52C
Mass flow rate is the amount of mass flowing through a crosssection per unit time whereas the
volume flow rate is the amount of volume flowing through a crosssection per unit time.
53C
The amount of mass or energy entering a control volume does not have to be equal to the amount of
mass or energy leaving during an unsteadyflow process.
54C
Flow through a control volume is steady when it involves no changes with time at any specified
position.
55C
No, a flow with the same volume flow rate at the inlet and the exit is not necessarily steady (unless
the density is constant). To be steady, the mass flow rate through the device must remain constant.
56E
A garden hose is used to fill a water bucket. The volume and mass flow rates of water, the filling
time, and the discharge velocity are to be determined.
Assumptions
1
Water is an incompressible substance.
2
Flow through the hose is steady.
3
There is no
waste of water by splashing.
Properties
We take the density of water to be 62.4 lbm/ft
3
(Table A3E).
Analysis
(
a
) The volume and mass flow rates of water are
/s
ft
0.04363
3
ft/s)
8
](
4
/
ft)
12
/
1
(
[
)
4
/
(
2
2
S
S
V
D
AV
V
&
lbm/s
2.72
/s)
ft
04363
.
0
)(
lbm/ft
4
.
62
(
m
3
3
V
&
&
U
(
b
) The time it takes to fill a 20gallon bucket is
s
61.3
¸
¸
¹
·
¨
¨
©
§
'
gal
4804
.
7
ft
1
/s
ft
0.04363
gal
20
3
3
V
V
&
t
(
c
) The average discharge velocity of water at the nozzle exit is
ft/s
32
]
4
/
ft)
12
/
5
.
0
(
[
/s
ft
04363
.
0
4
/
2
3
2
S
S
e
e
e
D
A
V
V
V
&
&
Discussion
Note that for a given flow rate, the average velocity is inversely proportional to the square of
the velocity. Therefore, when the diameter is reduced by half, the velocity quadruples.
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52
57
Air is accelerated in a nozzle. The mass flow rate and the exit area of the nozzle are to be determined.
Assumptions
Flow through the nozzle is steady.
Properties
The density of air is given to be 2.21
kg/m
3
at the inlet, and 0.762 kg/m
3
at the exit.
Analysis
(a) The mass flow rate of air is determined
from the inlet conditions to be
m
kg/s
0.796
)
m/s
0
4
)(
m
0.009
)(
kg/m
21
.
2
(
2
3
1
1
1
V
A
U
&
(
b
) There is only one inlet and one exit, and thus
&
&
m
m
1
2
.
Then the exit area of the nozzle is determined to be
&
m
V
1
= 40 m/s
A
1
= 90 cm
2
V
2
= 180 m/s
AIR
2
cm
58
m
0058
.
0
m/s)
)(180
m
kg/
(0.762
kg/s
0.796
2
3
2
2
2
2
2
2
¡o
¡
V
m
A
V
A
m
U
U
&
&
58
Air is expanded and is accelerated as it is heated by a hair dryer of constant diameter. The percent
increase in the velocity of air as it flows through the drier is to be determined.
Assumptions
Flow through the nozzle is steady.
Properties
The density of air is given to be 1.20 kg/m
3
at the inlet, and 1.05 kg/m
3
at the exit.
Analysis
There is only one inlet and one exit, and thus
. Then,
&
&
m
m
m
1
2
&
V
1
V
2
)
of
increase
and
(or,
1.14
kg/m
1.05
kg/m
1.20
3
3
2
1
1
2
2
2
1
1
2
1
14%
U
U
U
U
V
V
AV
AV
m
m
&
&
Therefore, the air velocity increases 14% as it flows through the hair drier.
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 Fall '09
 ferrenberg
 Thermodynamics, Energy, Mass, Mass flow rate, Ein Eout Esystem

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