# Fan Affinity Laws

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

**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 Flow Capacity

The volume flow capacity of a centrifugal fan can be expressed as

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 as

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 - the affinity laws for **change in wheel velocity** can be simplified to

##### Volume Flow 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 is increased with
*10%* - the head is increased with
*21%* - the power is increased with
*33 %*

- if the volume flow capacity of an existing system is increased with *10%* - the power supply increases with 33% and the electrical motor and the 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 units use is consistent.

q_{1}- volume capacity - (m^{3}/s, gpm, cfm, ..)

dp_{1}- head or pressure (m, ft, Pa, psi, ..)

P_{1}- power (W, bhp)

n_{1}- initial wheel velocity (rpm)

n_{2}- final wheel velocity (rpm)

**Changing the Impeller Diameter**

If the wheel velocity is constant - the affinity laws for **change in impeller diameter** can be simplified 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.

q_{1}- volume capacity - (m^{3}/s, gpm, cfm, ..)

dp_{1}- head or pressure (m, ft, Pa, psi, ..)

P_{1}- power (W, bhp)

d_{1}- initial wheel diameter (m, in, ft ...)

d_{2}- final wheel diameter (m, in, ft ..)

### Equivalent Static Pressure

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 (Pa)*

*dp _{act} = actual pressure (Pa)*

*ρ _{std} = standard density of air (kg/m^{3})*

*ρ _{act} = actual density of air (kg/m^{3})*

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