The equations for calculation are given below

Compressor Efficiency Definitions

Several different measures of compressor efficiency are commonly used: volumetric efficiency, adiabatic efficiency, isothermal efficiency and mechanical efficiency.

Adiabatic and isothermal efficiencies are computed as the isothermal or adiabatic power divided by the actual power consumption. The figure obtained indicates the overall efficiency of compressor and drive motor.

Isothermal Efficiency

Isothermal power(kW) = P₁ x Q₁ x log_er/36.7

P₁ = Absolute intake pressure kg/ cm²

Q₁ = Free air delivered m³/hr.

r = Pressure ratio P₂/P₁

The calculation of isothermal power does not include power needed to overcome friction and generally gives an efficiency that is lower than adiabatic efficiency. The reported value of efficiency is normally the isothermal efficiency. This is an important consideration when selecting compressors based on reported values of efficiency.

Volumetric Efficiency

Compressor Displacement = P x D² x L x S x c x n

4

D = Cylinder bore, metre

L = Cylinder stroke, metre

S = Compressor speed rpm

c = 1 for single acting and

2 for double acting cylinders

n = No. of cylinders

To some extent you need to decide what the 'efficiency' figure is needed for.

GUEST has given an exact formula but with so many other factors involved that it makes an accurate figure almost impossible because a lot of the factors are based on assumptions. Your flow of 605.2 cfm quoted to one decimal place is suspicious to say the least.

If it is 'rule-of-thumb' you want, then an approximation should do. Everything else being made equal, the power required in terms of your working pressure will be proportional to log_e r (see Guest formula) where r is the pressure ratio - which is your delivery pressure divided by your atmospheric pressure (absolute).

for other calcs first you need to establish the accuracy of the numbers you insert in your formula - use those given by the compressor people

Then go to this link and read about how careful you must be when using the result of these 'accurate' figures.

http://www.cashflo.co.uk/Calc.html

You can then investigate the steps you must take to get nearer the efficiency you want for your own application.

Guest's formula in #1 is correct in some circs but not for most practical cases. What's needed is the polytropic power, given by

(P₁ x Q₁)/n*((P₂/P₁)ⁿ-1) watt in SI units, m³/sec and Pa. The "polytropic exponent" n = 0.23. This is the power needed to compress the air and comes to 104 kW. To calculate the compressor shaft power need to divide by compressor efficiency, could be 65% but supplier can confirm. Gives ~160 kW. 90 kW motor is too small.

Isothermal power comes to just over 75 kW so even in this case with typical compressor efficiency 90 kW motor is inadequate.

Re Codemaster detailed reply.

The conclusion that 90 kw is not big enough for 605.2 cfm, prompts one to ask what the output would be from a compressor fitted with a 90kw motor.

On a polytropic basis at 65% efficiency (typical and realistic) you get 340 cfm whereas on a an isothermal basis at 100% efficiency (highly unlikely) you get 726 cfm.

This does not answer the original question but it at least point to the things to look out for, and it all depends on the actual design of the compressor.

You would have to carry out actual tests in order to accurately compare compressors. And if you want to introduce some degree of consistency into your study you might find this standard useful:-

ISO 1217 - Displacement compressors -- Acceptance tests.

This will not solve your problem about the amount of air needed to operate your equipment. But at least it will remove a lot of guesswork when selecting the right compressor.

At the moment the sums suggest a compressor with a 90kw motor will not be big enough to run your equipment - if 605 cfm is the amount of air you want.