Compressors, Gas Turbines and Jet Engines
If the clearance ratio for a reciprocating air compressor is 'K', then its volumetric efficiency is given by

1 - k + k (p₁/p₂)1/n
1 - k + k (p₁/p₂) n- 1/n
1 + k - k (p₂/p₁)1/n
1 + k - k (p₂/p₁) n-1/n

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Compressors, Gas Turbines and Jet Engines
The assumption made in two stage compression with inter-cooler is that

There is no pressure drop in the inter-cooler
The suction and delivery of air takes place at constant pressure
All of the listed here
The compression in both the cylinders is polytropic

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