Compressors, Gas Turbines and Jet Engines
In jet propulsion power unit, the inlet duct of diverging shape is used in order to

Collect more air
Beautify the shape
Convert kinetic energy of air into pressure energy
Provide robust structure

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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
The compression in both the cylinders is polytropic
All of the listed here

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