Question

Air enters the compressor of a gas-turbine plant at ambient conditions of 100 kPa and 25°C with a low velocity and exits at 1 MPa and 347°C with a velocity of 90 m/s. The compressor is cooled at a rate of 1500 kJ/min, and the power input to the compressor is 250 kW. Determine the mass flow rate of air through the compressor.

Answer 1

Air is compressed by a compressor. The mass flow rate of air through the compressor is to be determined.

Assumptions:

1. This is a steady-flow process since there is no change with time.
2. Potential energy changes are negligible. 
3. Air is an ideal gas with variable specific heats.

Properties: The inlet and exit enthalpies of air are (Table A-17)

Analysis: We take the compressor as the system, which is a control volume since mass crosses the boundary. The energy balance for this steady-flow system can be expressed in the rate form as

Substituting, the mass flow rate is determined to be