Fan and Pump Affinity Laws

The Affinity Laws are a set of fundamental mathematical relationships that dictate how the performance characteristics of centrifugal machinery—specifically flow rate, pressure/head, and power—react when the operational speed or the physical size of the impeller is altered. By leveraging these laws, engineers can reliably forecast performance across varying conditions without physical testing, optimizing equipment sizing and calculating energy savings.

1. Fan Affinity Laws (Speed Changes)

These laws predict the operational shifts when the rotational speed (RPM) of a fan is adjusted, assuming air density and system geometry remain constant.

Flow vs Speed
Directly Proportional - Fan flow increases linearly with speed.

(Q₂ / Q₁) = (N₂ / N₁)

Pressure vs Speed
Fan pressure increases with the square of the speed.

(P₂ / P₁) = (N₂ / N₁)²

Power vs Speed
Power increases with the cube of speed.

(Pwr₂ / Pwr₁) = (N₂ / N₁)³

For example: If the fan speed is reduced to 80% = Cube of 0.8 = 0.512, power reduces by almost 51%. Hence the reason Variable Speed Drives (VSDs) produce massive energy savings.

Interactive Fan Speed Calculator

Input a percentage change (e.g., -20 or 10) into ANY box to calculate the corresponding effects.

Change in Speed N

Change in Flow Q

Change in Pressure P

Change in Power Pwr

2. Pump Affinity Laws (Speed Changes)

Similar to fans, variable speed drives (VSDs) on pumps allow engineers to accurately predict performance at varying speeds across hydronic systems.

Flow vs Speed
Flow rate is directly proportional to pump impeller speed.

(Q₂ / Q₁) = (N₂ / N₁)

Head vs Speed
The ratio of Heads is directly proportional to the square of the ratio of pump impeller speeds.

(H₂ / H₁) = (N₂ / N₁)²

Power vs Speed
The ratio of Pump powers is directly proportional to the cube of the ratio of pump impeller speeds. (The Cube Rule).

(Pwr₂ / Pwr₁) = (N₂ / N₁)³

Interactive Pump Speed Calculator

Input a percentage change into ANY box to calculate the corresponding effects.

Change in Speed N

Change in Flow Q

Change in Head H

Change in Power Pwr

3. Pump Affinity Laws (Impeller Diameter)

Reducing the diameter of a centrifugal pump impeller—while maintaining the same rotational speed—yields proportional shifts. Note: These relationships are generally valid down to approximately 90% of the original impeller diameter, as the pump casing stays constant and does not reduce in line with the impeller.

Flow vs Diameter
Flow rate is directly proportional to pump impeller diameter.

(Q₂ / Q₁) = (D₂ / D₁)

Head vs Diameter
Head is directly proportional to the square of the ratio of pump impeller diameters.

(H₂ / H₁) = (D₂ / D₁)²

Power vs Diameter
Power is directly proportional to the cube of the ratio of pump impeller diameters.

(Pwr₂ / Pwr₁) = (D₂ / D₁)³

Impeller Rules of Thumb

NPSH Required: Proportional to diameter. (NPSH₂ / NPSH₁ = D₂ / D₁)
Shaft Deflection: Proportional to diameter. (d₂ / d₁ = D₂ / D₁)
Piping Friction Loss: Proportional to 90% of the square of the diameters. (FL₂ / FL₁ = 0.9 × (D₂ / D₁)²)
Component Wear Rate: Proportional to the cube of the diameter. (WR₂ / WR₁ = (D₂ / D₁)³)

Interactive Diameter Change Calculator

Input a percentage change (e.g., -10) into ANY box to calculate the corresponding effects.

Diameter D

Flow & NPSH Q

Head H

Power & Wear Pwr

Practical Limitations

In actual practice, the pump affinity laws provide an approximation between flow, head and horsepower as pump impeller diameter or speed is varied. The values actually observed will vary somewhat less than predicted by the laws. That is, the actual exponents in the affinity equations are slightly less than their stated values and are different for each pump. This results from friction in hydraulic passages and impellers, leakage losses and variation of impeller discharge vane angles when diameters are changed. Pump manufacturers should be contacted to confirm actual impeller diameters and speed changes to meet new duty requirements.