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

m_f = 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