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Air Compressor Equation Help.

  1. Aug 31, 2011 #1
    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:
    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
  2. jcsd
  3. Aug 31, 2011 #2
    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 }


    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
  4. Aug 31, 2011 #3

    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
  5. Sep 1, 2011 #4
    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 !
  6. Sep 2, 2011 #5

    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.
    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!

    Last edited: Sep 2, 2011
  7. Sep 6, 2011 #6
    lingusit, just returned home from holiday travel. Will have a look during my lunch break tomorrow. Cheers.
  8. Sep 6, 2011 #7
    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
  9. Sep 8, 2011 #8

    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!.

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