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.
This head when multiplied by the volumetric flow of gas (Q) gives the compressor power equations.
Adiabatic efficiency for the compressor is calculated as,
Adiabatic efficiency, η = (Actual Polytropic work / Adiabatic work)
Polytropic efficiency or hydraulic efficiency for a compressor is represented by,