# 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

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**The Affinity Laws** for centrifugal pumps and fans are used to express the influence on volume capacity, head (pressure) and/or power consumption due to

- change in wheel
speed- revolutions per minute (rpm), and/or- geometrically similarity by 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*

q_{1}/ q_{2}= (n_{1}/ n_{2})(d_{1}/ d_{2})^{3}(1)

where

q= volume flow capacity (m^{3}/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

dp_{1}/ dp_{2}= (n_{1}/ n_{2})^{2}(d_{1}/ d_{2})^{2}(2)

where

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

#### Power

The power consumption of a centrifugal fan can be expressed as

P_{1}/ P_{2}= (n_{1}/ n_{2})^{3}(d_{1}/ d_{2})^{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

q_{1}/ q_{2}= (n_{1}/ n_{2}) (1a)

##### Head or Pressure

dp_{1}/ dp_{2}= (n_{1}/ n_{2})^{2}^{ }(2a)

##### Power

P_{1}/ P_{2}= (n_{1}/ n_{2})^{3}^{ }(3a)

**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.

**Changing the Impeller Diameter**

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

##### Volume Capacity

q_{1}/ q_{2}=(d_{1}/ d_{2})^{3}(1b)

##### Head or Pressure

dp_{1}/ dp_{2}=(d_{1}/ d_{2})^{2}(2b)

##### Power

P_{1}/ P_{2}=(d_{1}/ d_{2})^{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.

### 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 = dp _{act} ρ_{std} / ρ_{act} (4)*

*where *

*ESP = Equivalent Static Pressure*

*dp _{act} = actual pressure *

*ρ _{std} = standard density *

*ρ _{act} = actual density*

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

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