# Pump Affinity Laws

The Pump Affinity laws predict the affects of changing the speed of a centrifugal or rotary pump on flow rate, head and power. Being able to predict these affects allows the rotating equipment engineer to examine the effects before implementing the changes.

The laws can be summarised as follows

Flow rate is directly proportional to pump impeller speed, e.g.

F_{1} / F_{2} | = | rpm_{1} / rpm_{2} | where F = flow rate, and rpm = impeller speed |

The ratio of Heads is directly proportional to the square of the ratio of pump impeller speeds, e.g.

H_{1} / H_{2} | = | (rpm_{1} / rpm_{2})^{2} | where H = Head, and rpm = impeller speed |

The ratio of Pump powers is directly proportional to the cube of the ratio of pump impeller speeds, e.g.

P_{1} / P_{2} | = | (rpm_{1} / rpm_{2})^{3} | where P = Power, and rpm = impeller spd |

#### Changing Pump Impeller Diameter

Experience also shows, that within limits, reducing the diameter of a centrifugal pump impeller has similar effect to the above, i.e.

Flow rate is directly proportional to pump impeller diameter, e.g.

F_{1} / F_{2} | = | D_{1} / D_{2} | where F = flow rate, and D = impeller Diameter |

The ratio of Heads is directly proportional to the square of the ratio of pump impeller diameters e.g.

H_{1} / H_{2} | = | (D_{1} / D_{2})^{2} | where H = Head, and D = impeller Diameter |

The ratio of Pump powers is directly proportional to the cube of the ratio of pump impeller diameters

P_{1} / P_{2} | = | (D_{1} / D_{2})^{3} | where P = Power, and D = impeller Diameter |

These relationships for impeller diameter are approximately correct for impeller diameters down to 90% of the original size, since the pump casing stays constant and does not reduce in line with the impeller.

#### Rules of Thumb

The following rules of thumb have also been observed as a result of changing impeller diameters;

The net positive suction head required by the pump manufacturer is directly proportional to pump impeller diameter, e.g.

NPSH_{1} / NPSH_{2} | = | D_{1} / D_{2} | where NPSH=Net Positive Suction Head, and D = impeller Diameter |

The amount of shaft run out (deflection) is directly proportional to pump impeller diameter, e.g.

d_{1} / d_{2} | = | D_{1} / D_{2} | where d = deflection, and D = impeller Diameter |

The ratio of Piping friction loss is proportional to 90% of the square of the ratio of pump impeller diameters

FL_{1} / FL_{2} | = | 0.9x(D_{1} / D_{2})^{2} | where FL = Friction Loss, and D = impeller Diameter |

The ratio of Wear Rate of the components varies in proportional to the cube of the ratio of pump impeller diameters, e.g.

WR_{1} / WR_{2} | = | (D_{1} / D_{2})^{3} | where WR = Wear Rate, and D = impeller Diameter |

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