Introduction to Affinity Laws

Affinity Laws are equations of proportionality that show how changes in impeller
[D], or rotative speed [N], affect the pump capacity [Q], differential head
[H], and required brake horsepower [HP]. Affinity Laws are also known as Affinity

According to Affinity Laws (or Affinity Equations):

Capacity is directly proportional to impeller diameter, or speed:

Q2 = Q1 x [ D2 / D1 ]
2 = Q1 x [ N2 / N1 ]

Head is directly proportional to the square of impeller diameter, or speed:

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

Horsepower is directly proportional to the cube of impeller diameter , or speed:

HP2 = HP1 x [ D2 / D1 ] ^3
HP2 = HP1 x [ N2 / N1 ] ^3

If both diameter and speed are changed, the equations are combined to become:

Q2 = Q1  x  [(D2 x N2) / (D1 x N1)]

2 = H1  x  [(D2 x N2) / (D1 x N1)] ^2

HP2 = HP1  x  [(D2 x N2) / (D1 x N1)] ^3

The subscript 1 is for initial condition, subscript 2 is for new condition, and ^ is an
exponential symbol.

The equations can be rearranged to calculate either the diameter, or speed, if the
other parameters were known. The term
head refers to differential head, not the
discharge head.

The equations are valid for U.S. customary units, metric system, or other units that
consistent units are used in the calculations.

The affinity equations do not imply that an impeller diameter, or speed, can be
changed arbitrarily. There are certain limits on how much they can be increased,
or decreased. These limitations are discussed in separate articles.

The Affinity Laws are based on the same fundamentals as the Similarity Laws (or
Laws of Similitude.) The main difference is in their use and application. Affinity
Laws are used to predict the change in performance within the same pump,
whereas Similarity Laws (also known as Modeling Laws) are used to extrapolate
the performance of one pump to predict the performance of another pump of
similar geometric or kinematic model.


  • On what types of pumps are the affinity laws applicable?

  • The affinity laws are accurate only under what specific condition? What
    should be done if this condition were not met?

  • How should the equations be applied to viscous performance curves?

  • Are the equations applicable to reverse-running centrifugal pump acting as
    hydraulic power recovery turbine (HPRT)?

The answers to these questions are excluded in this beta version, and are
included in the full version, of this article.
Read more.   Send comments.

R: 06110-INTO
C: basics, operation
F: affinity laws
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