### Compressed Air Design Equations

Fluids Design Engineering Resources

The horse power required for adiabatic compression of air can be expressed as:

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

Where

HP = horsepower
N = number of compression stages
n =  1.00  to 1.41 exponent of the compression curve adiabatic expansion coefficient
P = Atmospheric pressure (psi) (14.7 psi at sea level)
P2 = absolute terminal pressure after compression (psi)
V = volume of air at atmospheric pressure (cfm)

Horsepower required to compress isothermally for free air to a known pressure:

HP = (144 P V / 33,000) x (loge(P2/P))

Natural logarithims can be determined by maultiplying common logarithims by 2.30259.

Work required to compress air:

Total work ft-lbs = 3.46 P1 V1 [(P2/P1)0.29 - 1)]

and

The total work required for isothermal compression is:

Total work, Ft-Lbs =  P1 V1 Loge (V1/V2)

Where:

V1 = Initial volume absolute pressure psi
V2 = Volume of compressed air
P1 – Initial absolute pressure psf
P2 = Absolute pressure psf

Cubic feet of either compressed air or free air:

cu.ft. comp. air X (psig + 14.7) = cu.ft. free air X 14.7

• cu.ft. comp. air [ Cubic Feet of Compressed Air ]
• cu.ft. free air [ Cubic Feet of Free Air ]

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