# Define Free Air Delivery for an air compressor

Free Air Delivery (FAD) is a common measure of the capacity of an air compressor. I have a question that comes at the end here. My question is a little different from what you might be expecting. So first, let me establish some basics so that we don't just get replies giving a version of the standard answer.

FAD is a flow rate of air derived from measurement at the outlet of the compressor, defined at the corresponding outlet pressure, e.g. 300 litres per minute @ 700kPa. However, FAD is not simply the raw flow rate measured at the discharge at this raised pressure. The measured flow at the outlet first has to be converted back using a formula, to be the equivalent flow rate that would be obtained if the pressure and temperature were the same as at the intake.

Put in other words, here is a quote from a guide put out by the German compressor manufacturer Kaeser:

The air delivery of a compressor (known also as the free air delivery or FAD) is the expanded volume of air it forces into the air main (network) over a given period of time. The correct method of measuring this volume is given in the following standards: ISO 1217, annex C and DIN 1945, Part 1, Appendix F. ... Proceed as follows to measure FAD: the temperature, atmospheric pressure and humidity must first be measured at the air inlet of the compressor package. Then, the maximum working pressure, temperature and volume of compressed air discharged from the compressor are measured. Finally, the volume V2 measured at the compressor outlet is referred back to the inlet conditions using the following equation ... The result is the free air delivery (FAD) of the compressor package. This figure is not to be confused with the airend delivery. $$V_1= \frac{V_2 \cdot P_2 \cdot T_1}{T_2 \cdot F_1}$$

Source: Kaeser "Compressed Air Engineering: Basic principles, tips and suggestions."

Note that F1 is a factor where

$$F1= p_1- (p_p \cdot F_{rel})$$ where

p1 = inlet pressure

pp = vapour pressure

Frel = inlet humidity

For teaching purposes, that is a quite a lot to take in at once. It would be good to state an initial, approximate, concept that can then be qualified and refined.

So, to my question. Is this not virtually the same as saying: "Aside from leakage losses, FAD is equivalent to the flow rate of air being sucked into the intake of a compressor that is working against a certain backpressure." Is that a legitimate statement?

Build up to the formula (is $F_2$ a typo for $P_2$?) one step at a time.

In the simplest situation, $V_1 = V_2$ (which should be obvious to everybody in the room).

But for a real compressor test, the inlet and outlet pressures will be different, so you need to correct for that using the ideal gas law.

And also the inlet and output temperatures will be different, so you need to correct for that as well.

And that's all there is to it!

A good way to reinforce the formula is to actually measure the flow rate, temperatures, and pressures, and show that the "correction factors" do matter in practice. For a small compressor, you should be able to find a way to measure $V_1$ directly at the inlet to verify the formula. Even if that slightly affects the compressor operation (e.g. attaching a pipe with a flow meter to the inlet), it shouldn't matter for the purpose of demonstrating what is going on.

Of course the mass flow in does equal the mass flow out, but that is just a different way of deriving the "complete" formula.

• Actually, F1 is a factor where $$F_1= p_1- (p_p \cdot F_{rel})$$ where p1 = inlet pressure, pp = vapour pressure, and Frel = inlet humidity – IanS Jul 13 '18 at 11:09
• I think the “mass flow in equals mass flow out” approach misses the F1 term, which is accounting for the moisture in the air by effectively reducing the air inlet pressure by the moisture partial pressure. Clearly, mass flow in = mass flow out, but only if you measure the condensed moisture. – Mark Aug 12 '18 at 14:55

I would suggest that since p, v and T are changing you should modify that statement to be about the mass flow input being equal to the mass flow output.

• Yes, I see what you mean. But it would introduce more concepts to explain right at the beginning, taking the edge off the practical side of things (e.g. for mechanics to grasp). An alternative would be to suggest that if the compressor is connected to a receiver tank, that the tank outlet is open just enough that input is balancing output and the pressure remains constant. It's a qualification but it deals in practical terms. Your thoughts? – IanS Jul 13 '18 at 10:27
• explain continuity first - I always go with a bath : the plug set to allow cold water to leave and the hot tap to provide just enough hot water coming in to keep the level the same and the temperature just so... Continuity of mass is so useful as a concept to explain how stuff like this works... – Solar Mike Jul 13 '18 at 10:32