Understanding Air Compressor Power Equations

[linguist]

Could someone help me with getting an understanding of the equations for the power required to compress air please.

I found this Calculator on the internet:
http://www.engineeringtoolbox.com/horsepower-compressed-air-d_1363.html
I am unsure if it is suitable or accurate enough etc. I see that it is for adiabatic compression & once again I am not sure if this is what I need & also the equation they have there is a little confusing to me at this stage.

For example, I would like to calculate the power required in kW to compress 10m^3 of air to 1172 kPa with a single stage compressor.


I am not really sure where to start so any help would be greatly appreciated so I can learn.

Thank You

 

[edgepflow]

These style of formulas are common and usually close enough for practical estimating. I think this formula gives the ideal (isentropic) power. Divide this by the efficiency to get the real "brake" power.

Also, you need to express your volume as a flow rate (the calculator is looking for cfm which is ft^3 / min). Convert your other units as needed to run the calculator.

A forumula I use that gives good (good enough that is) results is from "Analysis & Design of Energy Systems," Hodge, 2nd Edition, Eqn. 5-63, P. 354:

P-brake = mdot * cp * (T1 / eff) * { [ (P2 / P1 ) ^ (k-1)/k ] - 1 }

where,

P-brake = brake power for compressor
mdot = mass flow rate of fluid being compressed
cp = specific heat of gas being compressed
T1 = inlet temperature (use absolute temperature)
eff = compressor efficiency
P2 = outlet pressure
P1 = inlet pressure
k = adiabatic expansion coefficient

 

[linguist]

edgepflow,

Thanks very much for the reply, much appreciated.

Could I ask for a working example of the formula so I can see how to do it correctly.
I am not sure how to go about the the last part of the equation which is:
{ [ (P2 / P1 ) ^ (k-1)/k ] - 1 }

From a working example I can then see how to work it out.

Thanks Again

 

[edgepflow]

edgepflow,

Thanks very much for the reply, much appreciated.

Could I ask for a working example of the formula so I can see how to do it correctly.
I am not sure how to go about the the last part of the equation which is:
{ [ (P2 / P1 ) ^ (k-1)/k ] - 1 }

From a working example I can then see how to work it out.

Thanks Again

Suppose the outlet pressure is 8 times the inlet; then P2/P1 = 8.
For air, k = 1.4. Thus, k-1 / k = 0.286.

And P2/P1^(k-1)/k = 8^0.286 = 1.811 and finally

{ [ (P2 / P1 ) ^ (k-1)/k ] - 1 } = 1.811 - 1 = 0.811.

Now try this with your values !

 

[linguist]

edgepflow,

Thanks again, I can see how to calculate the second part of the equation.
I just went to try the calculation only to find out that I don't know what units are used for the first part of the equation.
Eg:
mdot = mass flow rate, is this in Cubic mtrs/min or ltrs/min or cfm etc?

T1 = inlet temperature, is this Celcius, Kelvin etc?


P2 = outlet pressure
P1 = inlet pressure , is this in kPa, Bar or psi etc?
I guess this is Absolute pressure & not Gauge?

If I use 1 as the cp = specific heat of gas being compressed is this correct?

The Answer in brake power, kW or Hp?

Thanks, sorry for the confusion on my part!

Cheers

 

[edgepflow]

edgepflow,

Thanks again, I can see how to calculate the second part of the equation.
I just went to try the calculation only to find out that I don't know what units are used for the first part of the equation.
Eg:
mdot = mass flow rate, is this in Cubic mtrs/min or ltrs/min or cfm etc?

T1 = inlet temperature, is this Celcius, Kelvin etc?


P2 = outlet pressure
P1 = inlet pressure , is this in kPa, Bar or psi etc?
I guess this is Absolute pressure & not Gauge?

If I use 1 as the cp = specific heat of gas being compressed is this correct?

The Answer in brake power, kW or Hp?

Thanks, sorry for the confusion on my part!

Cheers

lingusit, just returned home from holiday travel. Will have a look during my lunch break tomorrow. Cheers.

 

[edgepflow]

Consider the terms with units:

mdot * cp * T1

In general, this will be:

(mass / time) X (energy / mass-Temperature) X Temperature = Energy / Time = Power

So any units may be used. For example: take mdot (kg/sec), cp (Joule/kg-K), and T1 (K)

then we have:

kg/sec X (Joule / kg-K) X K = Joule /sec = watt

 

[linguist]

edgepflow,

Thanks very much for the reply, much appreciated!

I have been away for a couple of days myself.

I will do some calculations & see how I go.

Thanks very much once again, you have been of great assistance!.

Cheers