# Lesson Four - The Affinity Laws

The affinity laws of centrifugal pump performance express the effect on pump performance due to changes in certain application variables. The affinity law variables which affect pump performance are:

1) Pump speed in pump revolutions per minute (RPM).

2) Impeller diameter.

Changing the Pump Speed (RPM):

When the impeller diameter of a centrifugal pump is held constant the effect of changing the speed (RPM) of the pump is in accordance with the following:

Capacity: Q1/Q2 = N1/N2

Head: H1/H2 = (N1/N2)2

BHP: BHP1/BHP2 = (N1/N2)3

Where subset number 1 shows performance at the initial speed and subset number 2 shows performance at the new speed, and:

Q = Capacity, GPM

H = Head, Feet

BHP = Brake Horsepower

N = Pump Speed,RPM

Analysis: As shown from the above equations, changing the speed (RPM) of a pump affects the flow, head and input brake horsepower of the pump in different proportions. Changing the speed affects the flow through the pump by a proportion equal to the increase or decrease in speed. The pump head is changed by the square of the proportion of speed change, while the brake horsepower is changed by the cube of the proportion of speed change.

Changing the Impeller Diameter:

When the speed (RPM) of a centrifugal pump is held constant the effect of changing the impeller diameter (D) is as follows:

Capacity: Q1/Q2 = D1/D2

Head: H1/H2 = (D1/D2)2

BHP: BHP1/BHP2 = (D1/D2)3

Where subset number 1 shows performance at the initial impeller diameter and subset number 2 shows performance at the new impeller diameter, and:

Q = Capacity, GPM

H = Head, Feet

BHP = Brake Horsepower

D= Impeller Diameter

Analysis:

Analysis: As shown from the above equations, changing the diameter of a pump impeller affects the flow, head and input brake horsepower of the pump in different proportions. Changing the impeller diameter affects the flow through the pump by a proportion equal to the increase or decrease in diameter. The pump head is changed by the square of the proportion of diameter change, while the brake horsepower is changed by the cube of the proportion of diameter change.