Understanding Air Compressor Power Equations

In summary, In response to the question, "Could someone help me with getting an understanding of the equations for the power required to compress air please." the author found a calculator online that is suitable if the user understands the isentropic process. However, the author is unsure if this is what they need or if the equation is confusing. The author uses a formula from "Analysis & Design of Energy Systems," Hodge, 2nd Edition, Eqn. 5-63, P. 354 to calculate the power required. The brake power is expressed as mdot * cp * (T1 / eff). The efficiency of the compressor is also included in the equation. The author asks for a working example of the formula
  • #1
linguist
10
0
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
 
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  • #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 }

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
 
  • #3
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
 
  • #4
linguist said:
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 !
 
  • #5
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
 
Last edited:
  • #6
linguist said:
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.
 
  • #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
 
  • #8
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
 

1. What is the air compressor equation?

The air compressor equation, also known as the ideal gas law, is a mathematical formula that describes the relationship between pressure, volume, temperature, and amount of gas in a system. It is written as PV = nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the gas constant, and T is temperature.

2. How is the air compressor equation used?

The air compressor equation is used to calculate the properties of a gas in a closed system. It can be used to determine the pressure, volume, temperature, or amount of gas in a system, as long as three of the variables are known. It is commonly used in thermodynamics, chemistry, and engineering.

3. What are the units for the variables in the air compressor equation?

The units for pressure are typically in Pascals (Pa) or atmospheres (atm), volume in cubic meters (m^3), temperature in Kelvin (K), and number of moles in moles (mol). The gas constant, R, has different units depending on the units used for pressure, volume, and temperature. It can be found in various units such as Joules per mole-Kelvin (J/mol-K) or liters-atm per mole-Kelvin (L-atm/mol-K).

4. How does the air compressor equation relate to real-life situations?

The air compressor equation is a fundamental law of nature that helps us understand the behavior of gases in different conditions. It is used in a wide range of applications, such as calculating the pressure inside a tire, determining the amount of gas needed for a chemical reaction, or predicting the behavior of gases in weather systems. It is also used in the design and operation of air compressors, which are commonly used in manufacturing, construction, and other industries.

5. Are there any limitations to the air compressor equation?

The air compressor equation is based on the assumptions that the gas is ideal (no intermolecular forces), the particles are point masses, and there are no phase changes. These assumptions may not hold true in all situations, so the equation may not be accurate in all cases. Additionally, it is important to use consistent units and to ensure that the gas being analyzed is at a constant temperature and in a closed system.

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