Compressor Power Formulas
Air compressor formulas: the isothermal power for a free air delivery and pressure ratio, the shaft power with the efficiency and the receiver fill time.
The formulas
| To find | Formula |
|---|---|
| Isothermal power | Piso = p1 × Q × ln(r) |
| Shaft power | Pshaft = Piso / ηiso |
| Receiver fill time (from atmosphere) | t = V × (r − 1) / Q |
p1 is the intake pressure in pascals (101,325 Pa for atmosphere), Q the free air delivery in m³/s at the intake condition, r the ratio of the absolute outlet pressure to the intake pressure, V the receiver volume in m³ and ηiso the isothermal efficiency (the isothermal power divided by the shaft power). The isothermal power is the least power that any compressor needs, so a real one needs more. The efficiency of 0.65 and the other values are examples, and the maker gives the real figures. The fill time ignores the flow that the plant draws while the receiver fills.
Worked example: 0.1 m³/s of free air at a pressure ratio of 8
- Piso = 101,325 × 0.1 × ln 8 = 21.07 kW
- Pshaft = 21.07 / 0.65 = 32.42 kW
- A 0.5 m³ receiver fills in 0.5 × (8 − 1) / 0.1 = 35 s
Isothermal power for 0.1 m³/s
| Pressure ratio | Isothermal power |
|---|---|
| 4 : 1 | 14.05 kW |
| 6 : 1 | 18.16 kW |
| 8 : 1 | 21.07 kW |
| 10 : 1 | 23.33 kW |
Frequently asked questions
What is free air delivery?
The volume of air taken in per unit time, measured at the intake condition. It is the figure that gives the flow of a compressor on its data sheet.
Why is the isothermal power a minimum?
Compression at a constant temperature needs the least work. Real compressors heat the air, so they use more.
Does the pressure in the formula mean gauge or absolute?
The ratio r uses absolute pressures. A gauge pressure of 7 bar is about 8 bar absolute, which is a ratio of about 8.
Is the motor larger than the shaft power?
Yes. The motor needs a rating above the shaft power, and the drive losses add to it.
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