Theoretically the increase in volume is directly proportionate to the ratio of the absolute temperatures. So with the Rankin scale, 68F = 527.4R, therefore a 5F reduction in temp would increase the volume 1% (0.95% to be exact). The rule of thumb of 1% increase in volume for a 5F decrease is close because we are dividing by 500. Now the practical part – the oil coolant circuit with a contact cooled rotary is designed and controlled to maintain the coolant temperature above 180F (depends on the machine, manufacturer preference, pressure rating, and tolerance of the oil mixing thermo valve). Consequently, the air-end casting is normally operating at a temperature of 180 or higher. When the air enters the air-end, the temperature of the air is quickly elevated because the heat capacity of air is so low. As a result, the air entering the intake plenum of the element before the rotors turn to an intake closed position is not the same as the ambient air. That is why on a steady state application you do not see any significant change is compressor performance between day and night when the air temperature drops. Summer to winter will have a difference but it is also influenced by the cooler operating temperature of the compressor.
In summary, the change in volume associated with temperature assumes no external influences. To be accurate you would need to measure the change in air temperature at the intake plenum. It makes a difference but also depends on the compressor design, installation and temperature ranges.
There are so many standards out there today on the definition of SCFM.
SCFM is defined today by CAGI (Compressed Air and Gas Institute) as 14.5 psia, 68° F with 0% RH.
Some additional standards on the market today are 14.696, 70°F with 0% RH and 14.7 psia, 68°F with 0% RH. Some consider SFCM as NCFM (Normal cubic feet per minute) this is a 14.7 psia, 68°F with 36% RH.
All these different standards can be calculated using the same calculation. We just need to know what the starting point and ending points. As 1 bar equals 14.5 psia and 68° F equals 20° C is it reasonable that we use the current CAGI standard of 14.5 psia, 68° F with 0% RH as this will also cross over to the metric world simply.
So what or how does the effect the user or manufacture of the compressors. Simple stated if the compressor manufacture is stating their compressor produces 500 CFM as FAD (Free Air Delivery) @ 14.5 psia, 68° F with 0% RH doesn’t this mean that you get 500 CFM. The answer is no unless you’re inlet conditions equal 14.5 psia, 68° F with 0% RH and this is never the case. We must correct to the actual site conditions. Using Denver as an extreme with an altitude of 5280 Feet on a 90°F day with 45% RH the actual output of the compressor can be quite different then the name plate of the compressor.
ACFM = SCFM * ((Ps – (RHs * PVs)/ Pb -(RHa * PVa)) * (Ta/Ts) * (Pb/Pa)
Ps = Standard pressure (PSIA)
Pb = Atmospheric pressure – barometer (PSIA)
Pa = Actual pressure (PSIA)
RHs = Standard relative humidity
RHa = Actual relative humidity
PVs = Saturated vapor pressure of water at standard temperature (PSIa)
PVa = Saturated vapor pressure of water at actual temperature (PSIa)
Ts = Standard temperature (°R) NOTE: °R =°F+459.67
Given the example from Denver
ACFM =500 * ((14.5 – (0.0% * .3418)/(12.09 – (45% * .6988))) – ((90+459.67)/(68+459.67)) * (12.09/11.78)
This is gives us a 390 CFM. So if the requirement was 500 cfm and one purchased a 500 cfm Compressor rated at 14.5 psia, 68° F with 0% RH in Denver the end result would be that you where 22% short on the compressed air.
ICFM to ACFM
ICFM (Inlet Cubic Feet per Minute) is used by some compressor manufactures to covey conditions before additional items such as inlet filter, blower, or booster. If the pressures and temperatures are the same after the components then ACFM and ICFM are the same, but there are always pressure drops or rise will occur after the additional items listed.
The equation from ICFM to ACFM can be expressed as the follows:
ACFM = ICFM * ( Pact/ Pf) * (Tf / Tact)
Pact = pressure actual before filter or other items (PSIA)
Pf = pressure after filter or other items (PSIA)
Tf = Temperature after the filter or other items (°R)
Tact = Temperature actual before filter or other items (°R)
The ideal gas law is accurate at lower pressures and high temperatures. To account for pressure and temperatures deviation from the ideal situation the True Gas law or non-ideal gas law must be used.
PV = Z n R T
Z = Gas Compressibility factor
N = number of moles of gas present
This is especially handy when working gas mixtures.