Compressors, Gas Turbines and Jet Engines
If p₁ is the pressure of air entering the L.P, cylinder and p₃ is the pressure of air leaving the H.P. cylinder, then the ratio of cylinder diameters for a single acting, two stage reciprocating compressor with complete intercooling is given by

D₁/D₂ = (p₁ p₃)1/4
D₁/D₂ = (p₁ p₃)1/2
D₁/D₂ = (p₁/p₃)1/4
D₁/D₂ = (p₃/p₁)1/4

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Compressors, Gas Turbines and Jet Engines
The overall isothermal efficiency of the compressor is defined as the ratio of

Volume of free air delivery per stroke to the swept volume of the piston
Work required to compress the air isothermally to the actual work required to compress the air for the same pressure ratio
Isothermal power to the shaft power or B.P. of the motor or engine required to drive the compressor
Isentropic power to the power required to drive the compressor

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