Question

Air enters an adiabatic compressor at 100 kPa and 17 degrees Celsius at a rate of 2.4 m³/s, and it exits at 257 degrees Celsius. The compressor has anisentropic efficiency of 84 percent. Neglecting the changes in kinetic and potential energies, determine (a) the exit pressure of air and (b) thepower required to drive the compressor.

Answer 1

Draw the schematic figure of the compressor.

Convert the units of inlet temperature from Celsius to Kelvin.

Convert the units of inlet temperature from Celsius to Kelvin.

Obtain the properties of air at the inlet temperature of from Table A-17, “Ideal-gas properties of air,” from the text book.

Enthalpy,

Reduced pressure,

Obtain the properties of air at the exit temperature of from Table A-17, “Ideal-gas properties of air,” from the text book.

Enthalpy,

Write the relation or the isentropic efficiency of the compressor.

Here, is the isentropic enthalpy.

Substitute for , for , and for .

Obtain the reduced pressure corresponding to an enthalpy of from Table A-17, “Ideal-gas properties of air,” from the text book by interpolation.

(a)

Calculate the exit pressure of the air by using the following adiabatic relation:

Here, is the inlet pressure.

Substitute for , for , and for .

Therefore, the exit pressure of the air is .

(b)

Write the energy balance equation for a steady flow system.

Here, is the rate of net energy transfer by heat, work, and mass and is the rate of change in internal, kinetic, potential, energies.

Neglect the heat, kinetic and potential energies and rewrite the equation.

…… (1)

Here, is the power input to the compressor and is the mass flow rate.

Calculate the mass flow rate by using the following ideal gas equation:

Here, is the volumetric flow rate and is the gas constant for air.

Substitute for , for , for , and for .

Substitute for , for , and for in equation (1) to calculate the power input to the compressor.

Therefore, the power input to the compressor is .