Question

Air enter a compressor operating at steady state, the inlet conditions are P1=100 kPa, v1=0.85 m3/kg, C1=15 m/s, u1=120 kJ/kg. During the compression an amount of heat of 140 kJ/kg air is transferred from the air to the cooler and the air was delivered at P2=500 kPa, v2=0.17 m3/kg, C2=35 m/s, u2=210 kJ/kg. Determine the work required to the compression. What is the inlet to exit area?

Answer 1

The work required to compress the air is 230 kJ/kg. The inlet to exit area is 11.6 m^2/s.

The work required to compress the air can be calculated using the equation:

W = Hin - Hout

where W is the work, Hin is the enthalpy at the inlet, and Hout is the enthalpy at the outlet.

Substituting the given values:

W = u1 - u2 + Q

where Q is the heat transferred from the air to the cooler.

W = 210 kJ/kg - 120 kJ/kg + 140 kJ/kg = 230 kJ/kg

The inlet to exit area can be calculated using the equation:

A = v1/C1 = v2/C2

Substituting the given values:

A = 0.85 m3/kg / 15 m/s = 0.17 m3/kg / 35 m/s

A = 0.0567 m2/s / 0.0049 m2/s = 11.6 m2/s