Type a line (receiver 500 l 7 to 30 bar in 18 min; add rated 45 m3/h for the comparison, or give the rated FAD instead of the time for the fill time) or fill in the fields: the line and the fields stay in step.
Enter the volume of the starting air receiver, or of several filled together, the pressure at the start and at the end of the fill and the time it took, and the calculator gives the free air delivery (FAD) of the compressor: in m3/h, l/min and cfm. With the rated FAD from the compressor data it gives the per cent of rated and the fill time at the rated FAD; with the rated FAD alone, the fill time. The working is shown with your numbers, a drawing sets out the fill line, and the result is a line you can copy or add to a request.
Two assumptions: the air in the receiver is taken at the compressor intake temperature (isothermal ideal-gas arithmetic, with no temperature correction), and the atmospheric pressure is the standard atmosphere, 1.01325 bar(a), unless you enter the barometer reading. The result is the average delivery over the pressure range of the test. The calculator sets no acceptance limit and gives no class rule figures: compare the result with the compressor maker’s test procedure and the class requirement.
FAD = V x (p2 - p1) / (p0 x t). A 500 l receiver filled from 7 to 30 bar(g) in 18 min, with p0 = 1.01325 bar(a): the free air taken in is 0.5 m3 x 23 bar / 1.01325 bar = 11.35 m3, and 11.35 m3 / 18 min = 0.6305 m3/min, that is 37.83 m3/h, 630.5 l/min or 22.27 cfm. Between two gauge pressures p2 - p1 is the same as between the absolute ones.
per cent of rated = FAD from the test / rated FAD x 100. A 1 m3 receiver filled from 15 to 30 bar(g) in 12 min takes in 14.80 m3 of free air: 74.02 m3/h. Against a rated 150 m3/h that is 49.3 %, and at the rated FAD the fill would take 14.80 / 2.5 = 5.92 min. The calculator sets no acceptance limit: compare with the maker’s test procedure and the class requirement.
t = V x (p2 - p1) / (p0 x Q). Two 750 l receivers filled from 0 to 30 bar(g) at a rated 180 m3/h, that is 3 m3/min: 1.5 m3 x 30 bar / 1.01325 bar = 44.41 m3 of free air, and 44.41 / 3 = 14.80 min. That is the time if the compressor keeps the rated delivery over the whole pressure range.
| Quantity | Relation | Note |
|---|---|---|
| Free air | V free = V x (p2 - p1) / p0 | m3 at the inlet conditions; V the receiver volume, p2 - p1 the pressure rise |
| FAD from a test | Q = V x (p2 - p1) / (p0 x t) | m3/min with t in min; the average over the test |
| Per cent of rated | Q / Q rated x 100 | no acceptance limit is set here |
| Fill time at a rated FAD | t = V x (p2 - p1) / (p0 x Q) | if the delivery holds over the whole range |
| Absolute pressure | p(a) = p(g) + p0 | p0 the standard atmosphere, 1.01325 bar(a), an assumption, unless entered |
| Flow | 1 m3/min = 60 m3/h = 1000 l/min | 1 cfm = 0.028316846592 m3/min = 1.69901 m3/h |
| Pressure | 1 MPa = 10 bar | 1 psi = 0.06894757293168 bar; 1 kgf/cm2 = 0.980665 bar |
| Time and volume | 1 h = 60 min; 1 min = 60 s | 1 l = 0.001 m3 |
Gauge and absolute pressures differ by the atmospheric pressure p0, which no unit factor takes care of: p(a) = p(g) + p0. Unless entered, p0 is taken as the standard atmosphere, 1.01325 bar(a): an assumption.
The fill test formula, FAD = V x (p2 - p1) / (p0 x t), agrees in the compressed-air reference pages of two compressor makers (a tank pump-up method, and a worked filling example from the mass of air at the inlet conditions) and in a university engineering note that derives the filling time from a mass balance on the receiver. The free air delivery is referred to the inlet conditions of the compressor, as ISO 1217 defines it and as both maker pages describe it; a delivery at fixed reference conditions (Nm3/h, SCFM) is a different quantity. The isothermal arithmetic and the default atmospheric pressure, the standard atmosphere of 101325 Pa agreed internationally in 1954, are assumptions of this calculator. 1 psi = 6.894757293168 kPa, 1 kgf/cm2 = 98.0665 kPa, 1 l = 0.001 m3 and 1 cfm = 1 ft3/min = 0.028316846592 m3/min are exact by definition (the SI guide of a national metrology institute, and the international foot of 0.3048 m). The compressor maker’s test procedure and the class requirement always come first.
FAD = V x (p2 - p1) / (p0 x t): the receiver volume times the pressure rise, over the atmospheric pressure times the fill time. A 500 l receiver filled from 7 to 30 bar(g) in 18 min: 0.5 m3 x 23 bar / (1.01325 bar x 18 min) = 0.6305 m3/min, that is 37.83 m3/h, 630.5 l/min or 22.27 cfm. The free air taken in, 0.5 x 23 / 1.01325 = 11.35 m3, is the air at the inlet conditions that the compressor delivered during the test; divided by the time it gives the average delivery over the pressure range.
Either. Between two gauge pressures p2 - p1 is the same as between the matching absolute pressures, since both carry the same atmospheric pressure: 30 bar(g) - 7 bar(g) = 31.01325 bar(a) - 8.01325 bar(a) = 23 bar. A pressure without a mark is read as gauge, as the receiver gauge shows it; write bar(a), psia or a for an absolute pressure. When one pressure is gauge and the other absolute, the gauge one is made absolute by adding the atmospheric pressure, and the working says so.
The atmospheric pressure at the compressor inlet, p0, since the free air delivery is referred to the inlet conditions, as ISO 1217 defines it. Unless you enter it, the calculator takes the standard atmosphere, 1.01325 bar(a), as the air receiver calculator does, and labels it as an assumption. Where the barometer reads differently, or the compressor data state the rated FAD at another inlet pressure, enter that pressure (atm 1 bar). Deliveries in Nm3/h or SCFM refer to fixed reference conditions and are not taken.
The calculator sets no acceptance limit. It gives the delivery from the test as a per cent of the rated FAD entered, and the time the fill would take at the rated FAD, so the two can be set side by side. Whether a result is acceptable follows from the compressor maker’s test procedure and the class requirement, which always come first.
No. The arithmetic is isothermal, which is an assumption: the air in the receiver is taken at the compressor intake temperature, and no temperature correction is applied. A temperature written in the line is left out, and the result says so. The result is the average delivery over the pressure range of the test, from the start to the end pressure.
Volumes in l or m3, with a count of receivers filled together (2 x 750 l). Pressures in bar, mbar, kPa, MPa, psi (1 psi = 6.894757293168 kPa) or kgf/cm2 (98.0665 kPa exactly), each gauge or absolute. The fill time in h, min or s, also together (6 min 30 s). The rated FAD in m3/h, m3/min, l/min, l/s or cfm (1 cfm = 0.028316846592 m3/min, 1.699 m3/h). The atmospheric pressure in bar(a).
The calculator works out the delivery from the fill time only. When valves, rings, gaskets or other parts for the starting air compressor are needed, send the line from the calculator with a photograph of the compressor nameplate, and Vessel Core checks the details before an offer goes back.
