# Compressor Equation

Please give me the equation with a link if possible for determining power for a compressor. I know volume x pressure differential / efficiency but I think the gas being compressed also is a factor. Thank you.

## Answers and Replies

FredGarvin
Science Advisor
From my old thermo notes, a non-isentropic compressor has a power of:

$$\dot{W} = \frac{\dot{m}C_pT_1}{\eta_c} \left[\left(\frac{P_2}{P_1}\right)^{(\frac{\gamma-1}{\gamma})}-1\right]$$

You can see the same equation here:
http://www.grc.nasa.gov/WWW/K-12/airplane/compth.html

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The site seems to be down at the moment but there are online calculators for recips and centrifs at www.processassociates.com

To to process tools section.

Fred, from your equation a vacuum pump that has a 1bar/.01bar pressure ratio needs more power than a compressor that has a ratio of 10bar/1bar? Is m the molecular weight or the volume?

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FredGarvin
Science Advisor
m is mass flow rate.

I'll have to look around a bit, but a vacuum pump most likely will not be applicable here. I'm not sure, I don't deal with them.

Hello, I'm working on a model of a fan and I have the characteristic curves Flow/impelled power and flow/total pressure.

I also have the relation of adiabatic compression you have written but it concerns the Head (in meters) and not the mass flowrate. Therefore, my question is : how do you get the outlet pressure of a fan knowing the characteristic curves and the formula with the head ?

More clearly that possible to convert the Head (m) into a differential pressure (Pout-Pin) or even the outlet Pressure of the fan (Pout) ?

Thank you for any idea.

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Hi, somebody knows this formula???

HP= Q * 63 * Ln(Pd/Ps)

Is a rare formula that are been used in a pipeline gas.

Thanks.

Felipe

PD: Sorry if I make a mistake in the english, I speak spanish.

Fred, from your equation a vacuum pump that has a 1bar/.01bar pressure ratio needs more power than a compressor that has a ratio of 10bar/1bar? Is m the molecular weight or the volume?

$$\dot{m}$$ is the mass flow rate, & is equal to $$\rho$$$$\dot{V}$$

ie. work required also depends upon the inlet density.