# Horsepower required to Compress Air

## Calculate horsepower required by air compressors.

The horsepower required to adiabatic compression of air can be calculated with the calculator below:

*N - number of stages*

*V - volume flow of compressed air at atmospheric pressure (cfm, ft^{3}/min)*

*k - adiabatic expansion coefficient*

*P _{2} - absolute final pressure (psi)*

Theoretical horsepower required to compress one cubic foot of free air (atmospheric pressure) for single-staged, two-staged and three-staged compressors are indicated in the diagram below. In general - plus *15-20%* friction.

*1 cfm (ft*^{3}/min) = 1.7 m^{3}/h = 0.47 l/s = 28.3 l/min*1 psi (lb/in*^{2}) = 6894.8 Pa (N/m^{2}) = 6.895 10^{-2}bar*1 hp = 745.7 W*

The power required for adiabatic (process without transfer of heat) compression of air can be expressed as

HP = [144 N P_{1}V k / (33000 (k - 1))] [(P_{2 }/ P_{1})^{(k - 1)/N k}- 1] (1)

where

HP = horsepower

N = number of compression stages

k = 1.41 = adiabatic expansion coefficient

P_{1}= absolute initial atmospheric pressure (psi) (14.7 psi at sea level)

P_{2}= absolute final pressure after compression (psi)

V = volume of air at atmospheric pressure - standard or free air (scfm, ft^{3}/min)

- adiabatic compression (or expansion) takes place without transmission of heat