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:
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Q2 = Q1 x [D2/D1] |
Eq. (16) |
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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:
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H2 = H1 x [D2/D1]2 |
Eq. (18) |
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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:
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BHP2 = BHP1 x [D2/D1]3 |
Eq. (20) |
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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:
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Q2 = Q1 x [(D2 x N2)/(D1 x N1)] |
Eq. (22) |
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H2 = H1 x [(D2 x N2)/(D1 x N1)]2 |
Eq. (23) |
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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