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 Laws of Affinity Calculation Guide

The Affinity Laws:

The turbo machine affinity laws are common used for pumps and fans to calculate capacity, head and power consumption when changing speed or wheels diameters.

The Affinity Laws of a centrifugal pump or fan express the effect on capacity, head and power consumption of a pump or fan due to:
different speed - revolutions per minute (rpm)
geometrically similarity - impeller diameter

Changing the Pump or Fan Speed (rpm)
Changing the speed (rpm, rev/min) of the pump or fan:
Capacity
Q1 / Q2 = N1 / N2 (1)
Head
H1 / H2 = (N1 / N2)2 (2)
Power
P1 / P2 = (N1 / N2)3 (3)

where
Q = capacity
H = head
P = power
N = speed

If the speed increase with 10%
the volume increase 10%
the head increase 21%
the power increase 33 %
Note! This mean that if we want to increase the volume flow in an existing system with 10% we have to increase the power with 33%. In general the motor and the power supply must be changed.

Changing the Impeller Diameter
Changing the impeller diameter:
Capacity
Q1 / Q2 = D1 / D2 (4)
Head
H1 / H2 = (D1 / D2)2 (5)
Power
P1 / P2 = (D1 / D2)3 (6)
where
D = impeller diameter
Example - Pump Affinity Laws

Pump Speed Changed (Impeller Size 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 by transforming (1):
Q2 = Q1 N2 / N1 = (100 GPM) (3500 rpm) / (1750 rpm) = 200 GPM

The final head can be calculated by transforming (2):
H2 = H1 (N2 / N1)2 = (100 ft) ((3500 rpm) / (1750 rpm))2 = 400 ft

The final power consumption can be calculated by transforming (3):
P2 = P1 (N2 / N1)3 = (5 bhp) ((3500 rpm) / (1750 rpm))3 = 40 bph

Pump Impeller Diameter Changed (Pump Speed Constant)
The impeller diameter is changed from 8" (inch) to 6" (inch).
The final flow capacity can be calculated by transforming (4):
Q2 = Q1 D2 / D1 = ( 100 GPM) (6") / (8") = 75 GPM

The final head can be calculated by transforming (5):
H2 = H1 (D2 / D1)2 = (100 ft) ((6") / ( 8"))2 = 56,25 ft

The final power consumption can be calculated by transforming (6):
P2 = P1 (D2 / D1)3 = (5 bhp) ((6") / ( 8"))3 = 2,1 bph