Usefull Equations of Air compressor Systems

From Machinery's handbook (which is a common reference for oil flooded compressor engineers), the HP to compress the air adiabatically is:

HP = [144*N*P*V*n] / [33000 (n-1)] * [(P2/P)^[(n-1)/(N*n)] - 1]

where N = number of stages in which compressions is accomplished

P = atmoshperic pressure in pounds per square inch

P2 = absolute terminal pressure in pounds per ssquare inch

V = volume of air , in cubic feet, compressed per minute, at atmospheric pressure (this is the rated cfm of the machine typically and relates to the intake cfm)

n=exponent of the compression curve = 1.41 for adiabatic compression

This is the HP required at the compressor to compress the air. Now you have factors including efficiencies of the bearing system in the compressor, the motor efficiency, and the drivetrain efficiency that will add to the power required by the motor. For a given compressor you can simplify the problem by measuring the power consumption of the compressor, calculating the theoretical horsepower, and then back-calculating the efficiency of the machine. However, you should note that this efficiency can change with speed, inlet air temperature, oil temperatures (for an oil cooled compressor), etc.

And then you can use the following formulas for calculating the relationship between pressure and volume in adiabatic compression of air:

P2/P1 = (V1/V2)^1.41

where P1 = initial absolute pressure in lbs/ft^2

P2 = absolute pressure in lbs/ft^2 after compression

V1 = initial volume in cubic feet

V2 = volume in cubic feet after compression.

Hope all this helps.