The fan law for RPM is part of a group of relationships known as the fan affinity laws. These laws describe how airflow, pressure and power change when you alter the rotational speed of a geometrically similar fan running in the same gas. They are essential tools for engineers who adjust fan speed with variable-frequency drives in industrial and mining ventilation systems.
For a given fan (same diameter, same blades) operating in the same air density, the key fan laws related to RPM (speed) are:
- Airflow (Q) is directly proportional to speed (N): Q₂ / Q₁ = N₂ / N₁
- Pressure (P) is proportional to the square of speed: P₂ / P₁ = (N₂ / N₁)²
- Power (kW) is proportional to the cube of speed: kW₂ / kW₁ = (N₂ / N₁)³
These relationships show why RPM control is powerful but must be used carefully. For example, if you increase fan speed by 20% (N₂/N₁ = 1.2), the airflow increases by about 20%, pressure by about 44% (1.2²) and power by about 73% (1.2³). Conversely, reducing speed by 20% lowers power demand by nearly half, which is why variable-frequency drives can yield large energy savings in ventilation systems that rarely need full capacity.
In industrial plants and mines, the fan law for RPM is used when upgrading motors, adding VFDs, or checking whether an existing fan can handle a new duty. If you know the fan’s performance at one speed from its curve, you can approximate the curve at another speed by applying the affinity laws. This allows quick estimates of how much extra airflow you might gain or how much energy you might save by changing RPM.
It is important to remember the limits of the fan laws. They assume the fan stays within a similar aerodynamic regime and that the system resistance behaves in the normal way (pressure roughly proportional to flow squared). If a fan approaches stall, choking or structural limits, simple proportional relationships may no longer apply. Temperature changes and density differences in hot flue gas or deep mines also require corrections.
In summary, the fan law for RPM tells you that for a specific fan and gas, airflow varies directly with RPM, pressure varies with RPM squared and power varies with RPM cubed. These affinity laws underpin most speed-control decisions in industrial and mining ventilation engineering.
