CFM

I'm not exactly sure what you mean, but it sounds like how is SCFM (equivalent to free air delivery) affected by inlet temp when pumping against a constant outlet pressure. In that case, it depends on the defined temp for SCFM. SCFM is the equivalent volume per minute of perfectly dry air at atmospheric pressure (14.7 psi), and some defined temperature (usually 68° F, but sometimes 32° F) of a given CFM at some specified pressure and temperature.

If we assume the 68° F temperature, and perfectly dry air (0% humidity), an inlet temp below that would yield a higher SCFM (free air delivery), and air hotter than that would yield a lower value.

In other words, the higher the inlet temperature, the lower the SCFM produced at a constant pressure because the total displacement per minute of the compressor is constant, but the density of the air changes with temperature. Therefore with less mass of air per unit volume going in, you have less coming out, and less mass at the same pressure means less volume.

Using the Ideal Gas Law:

PV=nRT, where P = absolute pressure, V = volume, T = absolute temperature, n = number of moles, and R = the ideal gas constant. By dividing through by temperature, we get:

PV/T = nR If we now let V = the volume displaced by the compressor which is constant, and inlet and outlet pressures are constant, then we see that nR (mass of air in this case) is inversely proportional to the absolute temperature.

Another way to approach it is that:

P₁V₁ / T_{1 Inlet air} = P₂V₂ / T_{2 SCFM out.}

We will assume that the inlet condition is (dry air) at atmospheric pressure so that P₁ = P₂ we can divide both sides by P. We will define T₂ SCFM out as 68° F = 527.7° R and we can multiply both sides by that value, and converting T₁ to Rankine yields:

527.7*V₁ / (°F+459.7) _{(Inlet air)} = V_{2 (SCFM out)}

Since V₁ inlet will be a constant based on compressor displacement per minute, we observe that the SCFM will vary as the inverse of the absolute temperature of the inlet air.

Anurag

Free Air Delivery is a performance measurement of the air delivered by a compressor package at the discharge flange or outlet pipe of that package. It is expressed in terms of the inlet temperature and pressure of the compressor. In Europe and anywhere else that ISO sets the standards, free air delivery (FAD) is expressed as cubic meters per minute. In the United States, it is expressed as cubic feet per minute (cfm). In the United States, FAD is also known as ICFM or Inlet Cubic Feet per Minute. Why the air compression business does not use SCFM or Standard Cubic Meters per Minute, I don't know but I'm sure there is a very good reason.

While the temperature and pressure at the inlet is usually expressed as degrees Farenheit or Celsius and psig or bar, the calculations of the effects of temperature and pressure changes require conversion to Rankine or Kelvin and psia or bara. If you do not, the effects calculated will be incorrect.

Greg_G has done a pretty good job of explaining the calculations themselves using the Ideal Gas Law and Boyle's Law. Nice to participate with you again, Greg.