Fan Affinity Laws

Turbo machines affinity laws are used to calculate volume capacity, head or power consumption, when speed - rpm, or wheel diameters are changed for centrifugal fans

The Affinity Laws of centrifugal pumps or fans can be used to express the influence on volume capacity, head (pressure) or power consumption of a pump or fan due to

1. change in speed of wheel - revolutions per minute (rpm)
2. geometrically similarity - change in impeller diameter

Note that the affinity laws for pumps are not identical with fans.

Fan Affinity Laws

Volume Capacity

The volume capacity of a centrifugal pump can be expressed like

q₁ / q₂ = (n₁ / n₂)(d₁ / d₂)³ (1)

where

q = volume flow capacity (m³/s, gpm, cfm, ..)

n = wheel velocity - revolution per minute - (rpm)

d = wheel diameter

Head or Pressure

The head or pressure of a centrifugal pump can be expressed like

dp₁ / dp₂ = (n₁ / n₂)² (d₁ / d₂)² (2)

where

dp = head or pressure  (m, ft, Pa, psi, ..)

Power

The power consumption of a centrifugal pump can be expressed as

P₁ / P₂ = (n₁ / n₂)³ (d₁ / d₂)⁵ (3)

where

P = power (W, bhp, ..)

Changing the Wheel Velocity

If the wheel diameter is constant - change in fan wheel velocity can simplify the affinity laws to

Volume Capacity

q₁ / q₂ = (n₁ / n₂) (1a)

Head or Pressure

dp₁ / dp₂ = (n₁ / n₂)²  (2a)

Power

P₁ / P₂ = (n₁ / n₂)³  (3a)

Note! If the speed of a pump is increased with 10%

• the volume flow increases with 10%
• the head increases with 21%
• the power increases with 33 %

If we want to increase the volume flow capacity of an existing system with 10% we have to increase the power supply with 33%. In  this situation the electrical motor and power supply may need to be upgraded.

Fan Affinity Laws Calculator - Changing Wheel Velocity

Replace the default values with the actual values. The calculator is generic and can be used with all common units as long as the use is consistent. 

q₁ - volume capacity - (m³/s, gpm, cfm, ..)

dp₁ - head or pressure (m, ft, Pa, psi, ..)

P₁ - power (W, bhp)

n₁ - initial wheel velocity (rpm)

n₂ - final wheel velocity (rpm)

Changing the Impeller Diameter

If wheel velocity is constant a change in impeller diameter can simplify the affinity laws to

Volume Capacity

q₁ / q₂ = (d₁ / d₂)³ (1b)

Head or Pressure

dp₁ / dp₂ = (d₁ / d₂)² (2b)

Power

P₁ / P₂ = (d₁ / d₂)⁵ (3b)

Fan Affinity Laws Calculator - Changing Wheel Diameter

Replace the default values with the actual values. The calculator is generic and can be used with all common units as long as the use is consistent. 

q₁ - volume capacity - (m³/s, gpm, cfm, ..)

dp₁ - head or pressure (m, ft, Pa, psi, ..)

P₁ - power (W, bhp)

d₁ - initial wheel diameter (m, in, ft  ...)

d₂ - final wheel diameter (m, in, ft ..)

Resources, Tools and Basic Information for Engineering and Design of Technical Applications!

Web The Engineering ToolBox