6-125
6-150 Air is accelerated in a nozzle. The density of air at the nozzle exit is to be determined.
Assumptions Flow through the nozzle is steady.
Properties The density of air is given to be 4.18 kg/m3 at the inlet.
1
Analysis There is only one inlet and one exit, and thus m
m 1
U 1 A1V1
2
m
. Then,
m
m 2
1
U 2 A2V 2
A1 V1
U1
A2 V 2
U2
2
120 m/s
(4.18 kg/m 3 )
380 m/s
AIR
2
2.64 kg/m 3
Discussion Note that the density of air decreases considerably despite a decrease in the cross-sectional area
of the nozzle.
6-151 An air compressor consumes 4.5 kW of power to compress a specified rate of air. The flow work
required by the compressor is to be compared to the power used to increase the pressure of the air.
Assumptions 1 Flow through the compressor is steady. 2 Air is an ideal gas.
Properties The gas constant of air is 0.287 kPa·m3/kg·K (Table A-1).
1 MPa
300°C
Analysis The specific volume of the air at the inlet is
RT1
P1
v1
(0.287 kPa ˜ m 3 /kg ˜ K )(20 273 K )
120 kPa
0.7008 m 3 /kg
Compressor
The mass flow rate of the air is
V1
m
v1
0.010 m 3 /s
0.7008 m 3 /kg
120 kPa
20°C
0.01427 kg/s
Combining the flow work expression with the ideal gas equation of state gives the flow work as
wflow
P2v 2 P1v 1
R(T2 T1 )
(0.287 kJ/kg ˜ K)(300 20)K
80.36 kJ/kg
The flow power is
W flow
m wflow
(0.01427 kg/s)(80.36 kJ/kg) 1.147 kW
The remainder of compressor power input is used to increase the pressure of the air:
W
W total,in W flow
4.5 1.147
3.353 kW
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