Compressor Power and Efficiency Equations

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Gas compression can be expressed in terms of pressure and temperature variation as,
PVn = constant

A compression process typically following this pressure volume relation is known as polytropic process. If n=1, the process is isothermal (constant temperature). If n=γ=CP/CV, the compression is adiabatic compression (no heat exchange with the surrounding). Most gas compressions generally follow the adiabatic curve. Hence compressor equations are also based on adiabatic curve with n=γ,
PVγ = constant

Let subscripts 1 and 2 stand for inlet and outlet process conditions of the compressor. Then the pressure ratio of the compressor is P2/P1.
P2/P1 = (V1/V2)n … Polytropic compression
P2/P1 = (V1/V2)γ … Adiabatic compression

The head developed by the compressor is expressed in following compressor equations.

… Adiabatic compressor head equation

… Polytropic compressor head equation

This head when multiplied by the volumetric flow of gas (Q) gives the compressor power equations.

… Adiabatic compressor power equation

… Polytropic compressor power equation

Adiabatic efficiency for the compressor is calculated as,

Adiabatic efficiency, η = (Actual Polytropic work / Adiabatic work)

… Adiabatic efficiency equation

Polytropic efficiency or hydraulic efficiency for a compressor is represented by,

… Polytropic efficiency equation