For a two-stage reciprocating air compressor, for minimum work required the intercooler pressure is given by

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ISRO VSSC Technical Assistant Mechanical held on 08/02/2015

Option 1 : \({P_2} = \sqrt {{P_1} \times {P_3}} \)

ISRO VSSC Technical Assistant Mechanical held on 09/06/2019

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__Explanation:__

For maximum efficiency work consumption by the compressor should be minimum.

Intercooler:

- The intercooler is a constant pressure device which cools the working fluid at constant pressure.
- In a two or multistage air compressor, an intercooler is always placed between the low pressure (L.P.) and high pressure (H.P.) cylinder.
- The purpose of an intercooler is to reduce the work input given to the compressor to reach the same pressure as can be reached by a single compressor.
- Here in the below diagram, it can be clearly seen that using the intercooler green shaded region is the amount of work saved while compression by multi-staging.

where P1 = Intake pressure of air, P2 = Intercooler pressure, and P3 = Delivery pressure of air.

Minimum work input with perfect intercooling

For two-stage compressor

\(W = \frac{{2n}}{{n - 1}}{P_1}{V_1}\left[ {{{\left( {\frac{{{P_2}}}{{{P_1}}}} \right)}^{\frac{{n - 1}}{n}}} - 1} \right]\)

Now, \(\frac{{dW}}{{d{P_2}}} = 0\)

we get, \(P_2^2 = {P_1} \times {P_3}\)

\({P_2} = \sqrt {{P_1} \times {P_3}} \)

and also, \(\frac{{{P_2}}}{{{P_1}}} = \frac{{{P_3}}}{{{P_2}}}\)

Hence, **The pressure ratio per stage is equal and the intermediate pressure is the geometric mean of both the extreme pressures, \({P_2} = \sqrt {{P_1} \times {P_3}} \).**

__Important Points__

**Reciprocating compressors** are used to generate **very high pressure** even up to **1000 bar** which is not possible to obtain with the help of **rotary/ dynamic compressors**.