The three fan laws, also known as the fan affinity laws, describe how airflow, pressure and power change when the speed or size of a geometrically similar fan is altered. These simple relationships are fundamental to ventilation engineering and are widely used when selecting fans, adjusting speed with variable frequency drives or predicting the effect of system changes in industrial and mining applications.
For a given fan handling the same gas in the same system, the three basic fan laws with respect to speed (N) are:
- Airflow (Q) is proportional to speed: Q ∝ N
- Pressure (P) is proportional to speed squared: P ∝ N²
- Power (Pshaft) is proportional to speed cubed: Pshaft ∝ N³
This means that if you increase fan speed by 10%, airflow increases by about 10%, pressure by about 21% and power by about 33%, assuming the fan remains in a similar operating region and the system curve behaves normally. The reverse is also true: small reductions in speed can significantly reduce power consumption, which is why variable speed control is so effective for energy savings.
The same type of relationships can be written for changes in fan diameter when comparing geometrically similar fans. In that case, airflow is proportional to diameter cubed, pressure to diameter squared and power to diameter to the fifth power at the same speed. These scaling laws help engineers estimate how a larger or smaller fan of the same design will perform before detailed testing.
In practice, the three fan laws are used when applying variable frequency drives (VFDs) to ventilation fans. By reducing speed during periods of low demand, mines and industrial plants can reduce power consumption dramatically. The laws provide a quick estimate of how much airflow and power will change for a given speed adjustment. More detailed analysis then fine-tunes the operating point using fan curves and system curves.
It is important to remember that the fan laws are idealised relationships. They assume the fan is operating in a region where efficiency does not change significantly with speed and that the gas properties and system resistance follow normal patterns. At very low speeds, near stall or in systems with unusual characteristics, actual performance may deviate from the simple proportionalities, so fan curves and measurements are still needed.
In summary, the three fan laws state that airflow varies directly with speed, pressure with the square of speed and power with the cube of speed (and similar relationships apply for diameter changes). They are essential tools for predicting fan performance under different operating conditions in industrial and mining ventilation systems.
