Fan Affinity Laws.docx

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 1. change in wheel speed - revolutions per minute (rpm), and/or 2. 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 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 as 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 - the affinity laws for change in wheel velocity can be simplified to Volume Flow 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 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. 100

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

100

5

1750

3500

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 the wheel velocity is constant - the affinity laws for change in impeller diameter can be simplified 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. 100

100

5

8

6

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 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 where

(4)

ESP = Equivalent Static Pressure (Pa) dpact = actual pressure (Pa) ρstd = standard density of air (kg/m3) ρact = actual density of air (kg/m3) ESP can be useful when selecting fans from published data based on standard conditions.