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Engineering ToolBox > Pump Affinity Laws
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
- change in speed of wheel - revolutions per minute (rpm)
- geometrically similarity - change in impeller diameter
Note that the affinity laws for fans are not identical with pumps.
The volume capacity of a centrifugal pump can be expressed like
q1 / q2 = (n1 / n2)(d1 / d2) (1)
where
q = volume flow capacity (m3/s, gpm, cfm, ..)
n = wheel velocity - revolution per minute - (rpm)
d = wheel diameter
The head or pressure of a centrifugal pump can be expressed like
dp1 / dp2 = (n1 / n2)2 (d1 / d2)2 (2)
where
dp = head or pressure (m, ft, Pa, psi, ..)
The power consumption of a centrifugal pump can be expressed as
P1 / P2 = (n1 / n2)3 (d1 / d2)3 (3)
where
P = power (W, bhp, ..)
If the wheel diameter is constant - change in pump wheel velocity can simplify the affinity laws to
q1 / q2 = (n1 / n2) (1a)
dp1 / dp2 = (n1 / n2)2 (2a)
P1 / P2 = (n1 / n2)3 (3a)
Note! If the speed of a pump is increased with 10%
If we want to increase the volume flow capacity of an existing system with 10% we have to increase the power supply with 33%. In this situation the electrical motor and power supply may need to be upgraded.
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.
If wheel velocity is constant a change in impeller diameter can simplify the affinity laws to
q1 / q2 = d1 / d2 (1b)
dp1 / dp2 = (d1 / d2)2 (2b)
P1 / P2 = (d1 / d2)3 (3b)
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.
The pump speed is changed when the impeller size is constant. The initial flow is 100 gpm, the initial head is 100 ft, the initial power is 5 bhp, the initial speed is 1750 rpm and the final speed 3500 rpm.
The final flow capacity can be calculated with (1a):
q2 = q1 n2 / n1 = (100 gpm) (3500 rpm) / (1750 rpm) = 200 gpm
The final head can be calculated with (2a):
dp2 = dp1 (n2 / n1)2 = (100 ft) ((3500 rpm) / (1750 rpm))2 = 400 ft
The final power consumption can be calculated with (3a):
P2 = P1 (n2 / n1)3 = (5 bhp) ((3500 rpm) / (1750 rpm))3 = 40 bph
The diameter of the pump impeller is reduced when the pump speed is constant. The diameter is changed from 8 to 6 inches.
The final flow capacity can be calculated with (1b):
q2 = q1 (d2 / d1) = ( 100 gpm) ((¨6") / (8")) = 75 gpm
The final head can be calculated with (2b):
dp2 = dp1 (d2 / d1)2 = (100 ft) ((6") / ( 8"))2 = 56.3 ft
The final power consumption can be calculated with (3b):
P2 = P1 (d2 / d1)3 = (5 bhp) ((6") / ( 8"))3 = 2.1 bph