The fan laws in SI units
Let the speed ratio r equal new speed divided by old speed. With the same fan geometry and air density, Q₂ = Q₁ × r, Δp₂ = Δp₁ × r² and P₂ = P₁ × r³. Q is volumetric airflow, Δp is pressure and P is the power absorbed by the fan shaft at corresponding operating points.
Use the same units on each side: rpm for speed, m³/s or L/s for airflow, Pa for pressure and W or kW for power. These relations do not supply a missing starting duty. You need a valid measured or manufacturer-rated reference point.
The same-fan condition matters. Changing the impeller diameter, casing, blade geometry or inlet arrangement is not simply another speed adjustment. Ask for the applicable performance data for the changed equipment.
Fan laws calculation: a ten per cent speed increase
Consider an illustrative fan duty of 500 L/s at 300 Pa, absorbing 0.50 kW at the shaft. Increasing speed from 1,000 to 1,100 rpm gives r = 1.10. This example is arithmetic, not a Fumeflow rating or a proposed setting.
| Quantity | Calculation | Estimate |
|---|---|---|
| Airflow | 500 × 1.10 | 550 L/s |
| Pressure | 300 × 1.10² | 363 Pa |
| Shaft power | 0.50 × 1.10³ | 0.666 kW |
The power increase is about 33 per cent, even though speed rises by only ten per cent. Motor capacity, drive capacity, wheel speed and the permitted operating range therefore need checking before an adjustment.
A slower fan: what the cube law does and does not promise
At 80 per cent of the starting speed, the corresponding airflow ratio is 0.80, pressure ratio 0.64 and shaft-power ratio 0.512. Using the same illustrative starting point gives 400 L/s, 192 Pa and 0.256 kW.
This is not automatically a prediction of the electricity bill. Motor and controller losses, changing efficiency, hours of operation and the actual system duty affect electrical consumption. The laboratory still needs the airflow and containment required for its work.
Use the ratios to ask whether a lower-duty operating mode is worth assessing. The designer must then check the control sequence, minimum operating requirements and verification process. Read fan static efficiency for the distinction between air power, shaft power and electrical input.
Why the system curve still matters
The installed operating point sits where the fan curve and system resistance curve meet. A fan-law estimate describes corresponding points on the fan’s changed-speed performance. It does not make every point on an altered duct system behave the same way.
A new branch, dirty filter, moved damper, changed opening or altered inlet can change the system relationship. Pressure losses often vary approximately with flow squared over a suitable range, but a system can also have other pressure requirements. Establish the actual conditions before projecting a new duty.
Our guide to reading a fan curve explains the intersection. If the installation differs from the test arrangement, also consider fan system effect.
Check the assumptions before changing speed
Confirm the model, wheel, rotation, original speed and pressure basis. Record the air temperature and density conditions used for the performance data. At a corresponding operating point, a change in density changes pressure and power; do not mix a standard-air curve with unusual process conditions without correction.
- Check the fan’s maximum speed and permitted operating range.
- Check motor loading and the suitability of any speed controller.
- Review noise, vibration, bearings and the connected ductwork.
- Confirm the required cupboard or process performance after the change.
Keep the proposed settings, measurements and final accepted duty in the installation record. An estimate is a useful design step; commissioning establishes what the installed system actually delivers.
Questions about fan affinity laws
Does doubling fan speed double power?
For the same fan at corresponding points and comparable density, the cube law gives roughly eight times the shaft power. That makes motor and fan limits essential checks.
Can I use these laws to choose a larger impeller?
The examples here apply to a speed change on the same fan. A different wheel or casing needs the appropriate manufacturer selection data and similarity assumptions.