Compressors, Gas Turbines and Jet Engines
Surging is the phenomenon of

Air stream not able to follow the blade contour
Motion of air at sonic velocity
Air stream blocking the passage
Unsteady, periodic and reversed flow

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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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