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 0.5m^{3}/kg and 0.15m^{3}/kg correspondingly. Inlet and outlet lines are at same level.
Sol: Device: Centrifugal compressor Mass flow rate mf = 15Kg/min Condition at inlet:
V_{1} = 5m/sec; h_{1} = 5KJ/kg
Condition at exit:
V_{2} = 7.5m/sec; h_{3} = 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 = 0.025m^{2}
Now; Mass flow rate at outlet = mf_{2} = A_{2}.V_{2}/ν_{2}
15/60 = A_{2} × 7.5/0.15
Thus the ratio of inlet pipe diameter to outlet pipe diameter is 2.236