Question

An air compressor is operating at a steady state. The air enters at with a volumetric flow rate 1.2 m^3/s at 170 kPa and 22 degrees celsius with negligible velocity and leaves at 1500 kPa with velocity of 200 m/s. The power to the compressor is 60 kW and the compressor is cooled at a rate of 15 kJ/kg. Determine the exit area.

Answer 1

Good Morning Sir/Madam

The problem given is solved by using any of the two theorems given below:

1. CONSERVATION OF MASS (CONTINUITY

EQUATION)

2. CONSERVATION OF ENERGY (BERNOULI 's

EQUATION)

Coming to the data mentioned in the problem,

An Air Compressor is operating at steady rate.

At Inlet, Air enters with Flow rate Q_{​​​​​​i}​​​​​ = 1.2 cumec at pressure P_{​​​​​​I} = 170 KPa and temperature 22^o C

At outlet, Air leaves at Pressure P_{​​​​​​e} = 1500 KPa with a velocity V_{​​​​​​e} = 200 m/ sec

Also given Power to the compressor = 60KW and compressor is cooled at the rate of 15 KJ / Kg.

We 've to determine Exit Area or Outlet Area A_{​​​​​​e}.

As the Air Flow is steady Mass flow rate (m) into the compressor = Mass flow leaving the compressor i.e, Conservation of Mass principle.

Mathematically,

m​​​​​_i = m_{​​​​​​e}

Please follow the attachment given below:

Thanking you Sir/Madam