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 Affinity Laws:
Capacity, Q changes in direct proportion to impeller diameter D ratio, or to speed N ratio:
Q2 = Q1 x [D2/D1]
Q2 = Q1 x [N2/N1]
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
H2 = H1 x [N2/N1]2
BHP changes in direct proportion to the cube of impeller diameter ratio, or the cube of speed ratio:
BHP2 = BHP1 x [D2/D1]3
BHP2 = BHP1 x [N2/N1]3
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 [(D2xN2)/(D1xN1)]
H2 = H1 x [(D2xN2)/(D1xN1)]2
BHP2 = BHP1 x [(D2xN2)/(D1xN1)]3
This equation is 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.
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