# Fan Affinity Laws

** 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.

**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.

### 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.

## Related Topics

### • Ventilation Systems

Design of systems for ventilation and air handling - air change rates, ducts and pressure drops, charts and diagrams and more.

## Related Documents

### Belt Transmissions - Speed and Length of Belts

Calculate length and speed of belt and belt gearing.

### Fan AMCA Classification

Fan classification established by AMCA.

### Fan Capacity Diagrams

Pressure, head, air flow volume and fan capacity diagrams.

### Fans - Calculate Air and Brake Horsepower

AHP - Air Horse Power and BHP - Brake Horse Power.

### Fans - Troubleshooting

Guide to troubleshooting fan problems.

### Pumps - Affinity Laws

Turbo machines affinity laws can be used to calculate volume capacity, head or power consumption in centrifugal pumps when changing speed or wheel diameters.

### STP - Standard Temperature and Pressure and NTP - Normal Temperature and Pressure

The definition of STP - Standard Temperature and Pressure and NTP - Normal Temperature and Pressure.

### Types of Fans - Capacity Ranges

Centrifugal, axial and propeller fans and their capacity ranges.