Example using the Control Volume Energy Equation
Given
: A large air compressor takes in air at absolute pressure
P
1
= 14.0 psia, at temperature
T
1
= 80
o
F
(539.67 R), and with mass flow rate
= 20.0 lbm/s.
The diameter of the compressor inlet is
D
1
= 24.5
inches. At the outlet,
P
2
= 70.0 psia and
T
2
= 500
o
F
(959.67 R). The diameter of the compressor outlet is
D
2
= 7.50 inches. The shaft driving the compressor
supplies 3100 horsepower to the compressor.
m
±
(a)
To do
: Calculate the average velocity of the air
entering the compressor.
Solution
: At the inlet,
mV
1, avg
1, avg
1
1
1
1
A
V
A
ρ
≈=
±
where
the subscripts “avg” have been dropped for convenience. Thus,
1
1
2
11
4
4
2
RTm
mm
ADP
D
ρπρ
π
==
=
±
±±
V
, where
we have used the ideal gas law
PR
T
=
to calculate the density of the air. Substitution of the values
yields
2
ft lbf
53.34
539.67 R
lbm R
lbf
14.0
24.5
in
⋅
⋅
V
V
2
P
1
V
1
P
2
Compressor
D
1
D
2
Input shaft power
ω
V
2
()
1
1
2
2
lbm
4
20.0
4
ft
s
87.229
s
in
RT m
PD
=
≈
ft
87.2
s
±
(b)
To do
: Calculate the average velocity of the air leaving the compressor.
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 Fall '05
 CIMBALA
 Thermodynamics, 4m, 7.50 inches, 331.051 ft, 3100 horsepower

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