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Estimate temperature of air at exit from compressor:
The air compressor compresses atmospheric air at 0.1MPa and 270C 10 times the inlet pressure. During compression heat loss to surrounding is estimated to be 5 percent of compression work. Air enters compressor with the velocity of 40m/sec and leaves with 100m/sec. The inlet and exit cross section area are 100cm2 and 20cm2 respectively. Estimate temperature of air at exit from compressor and power input to the compressor.
Sol: Given that;
At inlet: P1 = 0.1MPa; T1 = 27 + 273 = 300K; V1 = 40m/sec; A1 = 100cm2
At exit: P2 = 10P1 = 1.0MPa; V2 = 100m/sec; A2 = 20cm2
Heat lost to surrounding = 5 percent of compressor work
As Mass flow rate mf = A1.V1/ 1 = A2.V2/ 2;
From equation (2) mf = (100 × 10-4 × 40)/ 0.8601 = 0.465kg/sec
mf = 0.465kg/sec
By applying SFEE to control volume:
negative sign is inserted as the work is done on the system
WS = -592.44 KJ/sec .......ANS
-ive sign shows work done on system
-Power input required to run compressor is 592.44KW
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