Methane is compressed in a twostage doubleacting compressor

Methane is compressed in a two-stage, double-acting compressor which is electrically driven at 165 rpm. The low pressure cylinder (30.5 times 35.5 cm) receives 6.86 cu m per minute of air at 96.53 kPa, 43.3 degree C, and the high pressure cylinder (20.3 times 35.5 cm) discharges the methane at 717.06 kPa. The isothermal overall efficiency is 74%. Find n_v and the kW output of the motor.

Solution

Pressure ratio across each stage of the compressor()=(p4/p1)^(1/N)

where p4=final pressure(717.06kpa);p1=initial pressure(96.53kpa);N=no.of cylinders(2)

=(717.06/96.53)^.5 =2.7255

(isothermal)={p1*v1*ln(p4/p1)}/{x*p1*v1*[(()^(1/x)-1]} where x=N*n/(n-1)

0.74 ={ln(717.06/96.53)}/{x*[(2.7255^(1/x)-1]}

=>x~0.57==>n~0.221

Total Power output of the motor is given by total work done by the two compressors per sec

=x*p1*v1*[ {()^(1/x)}-1]

=.57*96.53*(6.86/60)*[{(2.7255)^(1/.57)}-1]

=30.15 kw