Fans
Fan affinity laws (change of speed)
- where
- air flow rate before and after (m³/s)
- fan speed before and after (rpm)
- fan pressure before and after (Pa)
- fan absorbed power before and after (kW)
Explain this equation
Predicts how airflow, pressure and power change when a fan's speed is changed on the same system. Use it when re-pulleying a fan or setting an inverter during commissioning.
N₂/N₁ is the speed ratio. Q is airflow, p the fan pressure and P the absorbed power, each with 1 for before and 2 for after.
Each blade pass moves a fixed volume, so flow rises in step with speed. Pressure depends on velocity squared, so it rises with the square. Power is flow times pressure, so it goes with the cube.
Sense check: slowing a fan by 20 % gives 80 % flow, 64 % pressure and about 51 % power. That cube law is why fan speed control saves so much energy.
Watch out: the laws only hold if the system resistance is unchanged; moving dampers or dirty filters put the fan on a different curve.
Predicts flow, pressure and power when the speed of a fan on the same system changes, for example after a pulley change or inverter setting.
Enter your values to see the result.
Good to know
Flow is proportional to speed, pressure to speed squared and power to speed cubed. Cutting speed by 20 % cuts power by about half. Because the motor and drive efficiencies change at part load, real savings are a little less.
Common mistake
Applying the laws when the system itself has changed (dampers moved, filters loaded or VAV boxes throttled): the laws only hold along a fixed system curve.
Limits
Same fan, same air density, fixed system resistance (pressure proportional to flow squared). Systems with a fixed pressure component (e.g. constant-pressure control) do not follow the cube law.
Sources
Results are calculations from the published methods and figures shown, and depend on the data you enter. Follow the equipment manufacturer’s data, CIBSE guidance, BS EN 378, the F-gas Regulations and your company procedures. Refrigerant work needs the correct F-gas certification.