Type a line (receiver 500 l 10 to 30 bar compressor 60 m3/h; need 12 m3 free air 15 to 30 bar; 500 l 30 bar draw 3 m3) or fill in the fields: the line and the fields stay in step.
Enter the volume of an air receiver, or of several, the start and the end pressure and the free air delivery (FAD) of the compressor or other air supply, and the calculator gives the filling time and the free air the receiver takes in between the two pressures. In reverse, it gives the receiver volume for a stated amount of free air, or the pressure left after a stated draw. The working is shown with your numbers, a drawing sets out the pressure band to scale, and the result is a line you can copy or add to a request.
Isothermal ideal-gas arithmetic only: real filling takes longer, as the air warms when compressed and the delivery of the air supply falls as the pressure rises. The calculator gives no number of engine starts, no class rule figures and no safety valve settings; the maker data of the air supply and the engine and the class society rules govern any starting-air capacity.
free air = V x (p2 - p1) / p_atm = 0.5 m3 x 20 bar / 1.01325 bar = 9.87 m3 for a 500 l receiver from 10 to 30 bar(g); with an air supply of 1 m3/min FAD the time is t = 9.87 m3 / 1 m3/min = 9.87 min. Between two gauge pressures p2 - p1 is the same as between the absolute ones.
V = free air x p_atm / (p2 - p1): 12 m3 of free air between 15 and 30 bar(g) needs 12 x 1.01325 / 15 = 0.8106 m3, about 811 l in all.
pressure fall = free air x p_atm / V: 3 m3 drawn from 500 l at 30 bar(g) is 3 x 1.01325 / 0.5 = 6.08 bar, so about 23.92 bar(g) is left. A draw larger than the receiver gives down to atmospheric pressure is refused.
| Unit | Equals | Basis |
|---|---|---|
| 1 psi | 6.894757293168 kPa = 0.06894757293168 bar | a force of 1 pound on 1 square inch |
| 1 kgf/cm2 (at) | 98.0665 kPa = 0.980665 bar | standard gravity, 9.80665 m/s2 |
| 1 MPa; 1 kPa | 10 bar; 0.01 bar | the bar: 1 bar = 100 kPa |
| Standard atmosphere | 1.01325 bar(a) = 101.325 kPa | the default atmospheric pressure |
| 1 ft3 | 0.028316846592 m3 = 28.316846592 l | 1 ft = 0.3048 m |
| 1 l | 0.001 m3 | the litre |
| 1 cfm | 1 ft3/min = 0.028316846592 m3/min | cubic foot per minute |
| 1 l/s; 1 m3/h | 0.06 m3/min; 1/60 m3/min | 60 s in a minute, 60 min in an hour |
Gauge and absolute pressures differ by the atmospheric pressure, which no unit factor takes care of: p(a) = p(g) + p_atm.
The arithmetic is the ideal gas law at a constant temperature: the free air between two pressures is V x (p2 - p1) / p_atm, and the filling time is that free air over the free air delivery of the air supply. The filling time formula agrees in the compressed-air handbook of a compressor maker (a worked filling example) and in a university engineering note that derives it from a mass balance on the receiver; the delivery referred to the inlet conditions is the definition of ISO 1217, as a compressor maker and an energy-efficiency body give it. The standard atmosphere, 101325 Pa, was fixed by the General Conference on Weights and Measures (1954); 1 psi = 6.894757293168 kPa, 1 kgf/cm2 = 98.0665 kPa, 1 ft3 = 0.028316846592 m3 and 1 l = 0.001 m3 are exact by definition (NIST SP 811 and the SI brochure). The maker data of the air supply and the class society rules always come first.
The time is t = V x (p2 - p1) / (p_atm x Q): the receiver volume times the pressure rise, over the atmospheric pressure times the free air delivery (FAD) of the air supply. A 500 l receiver filled from 10 to 30 bar(g) by an air supply of 60 m3/h FAD, that is 1 m3/min: 0.5 m3 x 20 bar / (1.01325 bar x 1 m3/min) = 9.87 min. The free air taken in is 0.5 x 20 / 1.01325 = 9.87 m3, and the time is that free air over the delivery. The arithmetic is isothermal: real filling takes longer, as the air warms when compressed and loses some pressure as it cools, and the delivery of the air supply falls as the pressure rises.
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) - 10 bar(g) = 31.01325 bar(a) - 11.01325 bar(a) = 20 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 free air delivery (FAD) is the delivery of a compressor referred to its inlet conditions, as ISO 1217 defines it, and it is the free air this calculator counts. The default atmospheric pressure is the standard atmosphere, 1.01325 bar(a). Where the maker data state the FAD at another inlet pressure, or the barometer reads differently, enter that pressure (atm 1 bar). Figures in Nm3/h or SCFM refer to other reference conditions and are not taken; take the FAD from the maker data at your end pressure.
Turn the formula round: V = V_free x p_atm / (p2 - p1). For 12 m3 of free air between 15 and 30 bar(g), 12 x 1.01325 / 15 = 0.8106 m3, about 811 l in all, which may be split over two or more receivers. The free-air quantity is yours to state: the calculator gives no number of engine starts and no class rule figures, and the engine maker data and the class society rules govern any starting-air capacity.
The fall is dp = V_free x p_atm / V. Drawing 3 m3 of free air from a 500 l receiver at 30 bar(g): 3 x 1.01325 / 0.5 = 6.08 bar, so about 23.92 bar(g) is left. The receiver holds 0.5 x 30 / 1.01325 = 14.8 m3 of free air above atmospheric pressure at 30 bar(g); a larger draw is refused. Add the delivery of the air supply and the calculator gives the time to put the draw back.
Volumes in l, m3 or ft3 (1 ft3 = 0.028316846592 m3 exactly), with a count of receivers (2 x 250 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 delivery in m3/min, m3/h, l/s, l/min or cfm (cubic feet per minute). The free air in m3, l or ft3, and the atmospheric pressure in bar(a).
The calculator works out volumes, pressures and times only. When an air receiver, its valves, a safety valve or compressor parts are needed, send the line from the calculator with a photograph of the receiver nameplate and the compressor plate, and Vessel Core checks the details before an offer goes back.
