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: P_{1} = 0.1MPa; T_{1} = 27 + 273 = 300K; V_{1} = 40m/sec; A_{1} = 100cm^{2}
At exit: P_{2} = 10P_{1} = 1.0MPa; V_{2} = 100m/sec; A2 = 20cm^{2}
Heat lost to surrounding = 5 percent of compressor work
As Mass flow rate mf = A_{1}.V_{1}/ 1 = A_{2}.V_{2}/ 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