Fan Formulas: Air Power and Affinity Laws
Fan formulas: air power from flow and pressure, shaft power from fan efficiency, and the affinity laws for flow, pressure and power when speed changes.
The formulas
| To find | Formula |
|---|---|
| Air power | Pair (kW) = Q × Δp / 1000 |
| Shaft power | Pshaft = Pair / ηfan |
| Flow at a new speed | Q2 = Q1 × (N2 / N1) |
| Pressure at a new speed | Δp2 = Δp1 × (N2 / N1)² |
| Power at a new speed | P2 = P1 × (N2 / N1)³ |
Q is the flow in m³/s, Δp the total pressure rise in pascals and η the fan efficiency as a fraction (use the total or static value that matches your Δp). The affinity laws hold for the same fan and system, and they are an approximation when the system has a static pressure that does not change with flow.
Worked example: 2 m³/s at 800 Pa
The fan efficiency is 65%.
- Pair = 2 × 800 / 1000 = 1.6 kW
- Pshaft = 1.6 / 0.65 = 2.462 kW
Worked example: speed reduced to 80%
A drive slows the same fan from 50 Hz to 40 Hz, a speed ratio of 0.8.
- Q2 = 2 × 0.8 = 1.6 m³/s
- Δp2 = 800 × 0.8² = 512 Pa
- P2 = 2.462 × 0.8³ = 1.26 kW, which is 51.2% of the original power
Affinity laws by speed
| Speed | Flow | Pressure | Power |
|---|---|---|---|
| 100% | 100% | 100% | 100% |
| 90% | 90% | 81% | 72.9% |
| 80% | 80% | 64% | 51.2% |
| 70% | 70% | 49% | 34.3% |
| 50% | 50% | 25% | 12.5% |
Frequently asked questions
Why does a small speed cut save so much power?
Power varies with the cube of the speed. A 20% cut in speed gives about half the power.
Does the same law apply to pumps?
Yes, for the same pump and system. Flow follows the speed, head the square of the speed and power the cube.
What about a system with static head or a closed damper?
The system curve does not follow the square law then, so the saving is smaller. Use the fan curve and the system curve to find the new duty point.
Does the drive have losses?
Yes. A variable-speed drive has its own efficiency, usually a few percent, and the motor efficiency falls at low load.
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