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Air Compressor Equation Help. 
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#1
Aug3111, 03:43 AM

P: 10

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/ho...ird_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 


#2
Aug3111, 02:39 PM

P: 688

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. 563, P. 354: Pbrake = mdot * cp * (T1 / eff) * { [ (P2 / P1 ) ^ (k1)/k ]  1 } where, Pbrake = 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 


#3
Aug3111, 04:56 PM

P: 10

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 ) ^ (k1)/k ]  1 } From a working example I can then see how to work it out. Thanks Again 


#4
Sep111, 12:03 AM

P: 688

Air Compressor Equation Help.
For air, k = 1.4. Thus, k1 / k = 0.286. And P2/P1^(k1)/k = 8^0.286 = 1.811 and finally { [ (P2 / P1 ) ^ (k1)/k ]  1 } = 1.811  1 = 0.811. Now try this with your values ! 


#5
Sep211, 01:22 AM

P: 10

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 


#6
Sep611, 12:07 AM

P: 688




#7
Sep611, 02:32 PM

P: 688

Consider the terms with units:
mdot * cp * T1 In general, this will be: (mass / time) X (energy / massTemperature) X Temperature = Energy / Time = Power So any units may be used. For example: take mdot (kg/sec), cp (Joule/kgK), and T1 (K) then we have: kg/sec X (Joule / kgK) X K = Joule /sec = watt 


#8
Sep811, 05:54 PM

P: 10

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 


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