Fan Affinity Laws

Affinity laws can be used to calculate volume capacity, head or power consumption - when speed or rpm, and wheel diameters are changed

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 fan 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 fan 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 fan 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)

 

fan affinity laws velocity diagram

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

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

If the volume flow capacity of an existing system is increased with 10% the power supply is increased with 33%. The electrical motor and power supply may need an upgrade.

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 diameter diagram

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 ..)

Equivalent Static Pressure

The use of the fan laws can sometimes be simplified by using Equivalent Static Pressure - ESP - defined as the pressure that would be developed by a fan operating at standard air density instead of the actual air density.

ESP = dpact ρstd / ρact  (4)

where

ESP = Equivalent Static Pressure

dpact = actual pressure

ρstd = standard density 

ρact  = actual density

ESP can be useful when selecting fans from published data based on standard conditions.

Related Topics

  • Ventilation - Systems for ventilation and air handling - air change rates, ducts and pressure drops, charts and diagrams and more

Related Documents

Tag Search

  • en: fan affinity laws diameter speed pressure
  • es: ventilador leyes de afinidad presión velocidad diámetro
  • de: Fan Affinitätsgesetze Durchmesser Geschwindigkeit Druck

Search the Engineering ToolBox

- "Search is the most efficient way to navigate the Engineering ToolBox!"

Engineering ToolBox - SketchUp Extension - Online 3D modeling!

3D Engineering ToolBox Extension to SketchUp - add parametric components to your SketchUp model

Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your SketchUp model with the Engineering ToolBox - SketchUp Extension/Plugin - enabled for use with the amazing, fun and free SketchUp Make and SketchUp Pro. Add the Engineering ToolBox extension to your SketchUp from the Sketchup Extension Warehouse!

Translate the Engineering ToolBox!
About the Engineering ToolBox!

close