# Problem: Sizing a Two-Stage Air Compressor Given: A two-stage air compressor with an intercooler

System Pressure: 120 PSIG. Each stage raises the pressure 60 PSI.

Initial air temperature: 70° F

Entering air temperature at second stage: 90° F

First stage: 3” diameter x 4” stroke

Neglect the volume of the intercooler. After the first revolution, the air is just passing through.

Find the required diameter for the second stage with the same 4” stroke.

##### See the Solution

One possible solution is to use the following formula:

P1 x V1 x T2 = P2 x V2 x T1

V2 = P1 x V1 x T2
P2 x T1

P1 = Initial Absolute Pressure
P2 = Final Absolute Pressure

V1 = Initial Volume
V2 = Final Volume

T2 = Final Absolute Temperature
T1 = Initial Absolute Temperature

P1 = 14.7 PSIA
V1 = 3² x .7854 x 4” = 28.27 in³
T2 = 90 + 460 or 550° Rankine (Absolute F.)
P2 = 60 + 14.7 or 74.7 PSIA
T1 = 70° + 460 or 530° Rankine
V2 = Unknown

V2 = 14.7 x 28.27 x 550
74.7 x 530

V2 = 5.77 in³
A = Volume / Stroke
5.77 / 4 = 1.44 in²
A = D² x .7854
D = 1.36”

### Deadline past. Not available for submissions.

By Ernie Parker, CFPAI, CFPSD, CFPS, CFPMM, CFPMT, CFPMIP, CFPMMH, CFPMIH

This teaser is printed in the Fluid Power Journal. Those who submit the correct answer before the deadline will have their names printed in the Society Page newsletter and in the Fluid Power Journal. The winners will also be entered into a drawing for a special gift.

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