Estimate temperature of air at exit from compressor , Mechanical Engineering

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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;

1726_Estimate temperature of air at exit from compressor.png

From equation (2) mf  = (100 × 10-4 × 40)/ 0.8601 = 0.465kg/sec

mf = 0.465kg/sec          

 By applying SFEE to control volume:

1357_Estimate temperature of air at exit from compressor1.png

negative sign is inserted as the work is done on the system

1308_Estimate temperature of air at exit from compressor2.png

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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