# The Affinity Laws

The Affinity Laws are mathematical expressions that define changes in pump capacity, head, and BHP when a change is made to pump speed, impeller diameter, or both. According to the Affinity Laws:

Capacity (Q) changes in direct proportion to impeller diameter D ratio, or to speed N ratio:

Q2 = Q1 x [D2/D1]

Eq. (16)

Q2 = Q1 x [N2/N1]

Eq. (17)

Head (H) changes in direct proportion to the square of impeller diameter D ratio, or the square of speed N ratio:

H2 = H1 x [D2/D1]2

Eq. (18)

H2 = H1 x [N2/N1]2

Eq. (19)

BHP changes in direct proportion to the cube of impeller diameter ratio, or the cube of speed ratio:

BHP2 = BHP1 x [D2/D1]3

Eq. (20)

BHP2 = BHP1 x [N2/N1]3

Eq. (21)

Where the subscript: 1 refers to initial condition, 2 refer to new condition.

If changes are made to both impeller diameter and pump speed the equations can be combined to:

Q2 = Q1 x [(D2 x N2)/(D1 x N1)]

Eq. (22)

H2 = H1 x [(D2 x N2)/(D1 x N1)]2

Eq. (23)

BHP2 = BHP1 x [(D2 x N2)/(D1 x N1)]3

Eq. (24)

These equations are used to hand-calculate the impeller trim diameter from a given pump performance curve at a bigger diameter.

The Affinity Laws are valid only under conditions of constant efficiency