### 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 [(P_{2} / 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)

P_{2} = 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 (log_{e}(P_{2}/P))

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

*Work required to compress air:*

Total work ft-lbs = 3.46 P_{1} V_{1} [(P_{2}/P_{1})^{0.29} - 1)]

and

The total work required for isothermal compression is:

Total work, Ft-Lbs = P_{1} V_{1} Log_{e} (V_{1}/V_{2})

Where:

V_{1} = Initial volume absolute pressure psi

V_{2} = Volume of compressed air

P_{1} – Initial absolute pressure psf

P_{2} = 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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