Centrifugal air compressor:

A centrifugal air compressor delivers 15Kg of air per minute. The outlet and inlet conditions are

At inlet: Velocity = 5m/sec, enthalpy = 5KJ/kg

At outlet: Velocity = 7.5m/sec, enthalpy = 173KJ/kg

Heat loss to the cooling water is 756KJ/min find:

(1)  The power of motor required to drive compressor.

(2)  Ratio of inlet pipe diameter to outlet pipe diameter when specific volumes of air at inlet and outlet are 0.5m³/kg and 0.15m³/kg correspondingly. Inlet and outlet lines are at same level.

Sol: Device: Centrifugal compressor Mass flow rate mf  = 15Kg/min Condition at inlet:

V₁  = 5m/sec; h₁  = 5KJ/kg

Condition at exit:

V₂  = 7.5m/sec; h₃  = 173KJ/kg

Heat loss to cooling water Q =  -756 KJ/min

From SFEE

WS= -3276.23KJ/min = - 54.60KJ/sec                              .......ANS

(negative sign indicate that work done on the system) Thus the power of motor required to drive the compressor is 54.60KW

Mass flow rate at inlet = Mass flow rate at outlet = 15kg/min = 15/60 kg/sec

Mass flow rate at inlet = mf1  = A1.V1/  ν1

15/60 = A1  × 5/0.5

A1  = 0.025m²

Now; Mass flow rate at outlet = mf₂  = A₂.V₂/ν₂

15/60 = A₂  × 7.5/0.15

Thus the ratio of inlet pipe diameter to outlet pipe diameter is 2.236