Pump Affinity Laws
The Pump Affinity law equations predict the effects 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 pump affinity laws can also be applied to fans, therefore it is not uncommon to see the affinity laws called the "fan laws".
Pump Affinity Law Formula
The pump laws, as they are sometimes called, can be neatly summarised by the following "Pump Affinity Law Formula"
Flow rate is directly proportional to pump impeller speed, e.g.
| F1 / F2 | = | rpm1 / rpm2 | 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.
| H1 / H2 | = | (rpm1 / rpm2)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. This affinity law is sometimes referred to as The Cube Rule, and is shown below;
| P1 / P2 | = | (rpm1 / rpm2)3 | where P = Power, and rpm = impeller speed |
Effect of 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.
| F1 / F2 | = | D1 / D2 | 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.
| H1 / H2 | = | (D1 / D2)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
| P1 / P2 | = | (D1 / D2)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.
Pump Impeller Rules of Thumb
The following rules of thumb have also been observed as a result of changing pump impeller diameters;
The net positive suction head required by the pump manufacturer is directly proportional to pump impeller diameter, e.g.
| NPSH1 / NPSH2 | = | D1 / D2 | 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.
| d1 / d2 | = | D1 / D2 | 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
| FL1 / FL2 | = | 0.9x(D1 / D2)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.
| WR1 / WR2 | = | (D1 / D2)3 | where WR = Wear Rate,
and D = impeller Diameter |
Limitations of Pump Affinity Laws
In actual practice, the pump affinity laws provide an approximation between flow, head and horsepower as pump impeller diameter or speed is varied. The values actually observed will vary somewhat less than predicted by the pump laws. That is, the actual exponents in the affinity equations are slightly less than their stated values and are different for each pump. This results from friction in hydraulic passages and impellers, leakage losses and variation of impeller discharge vane angles when diameters are changed. Pump manufacturers should be contacted to confirm actual impeller diameters and speed changes to meet new duty requirements.
Practical Application of Pump Affinity Laws
Variable speed drives (VSDs) are now being increasingly used for small pumps and are becoming more common for larger ones. Engineers can accurately predict the pump’s performance at varying speeds by applying affinity laws.
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