Rules of Thumb: Affinity Laws

Stephen Hall discusses the golden rules for design

AFFINITY laws are a set of relationships for rotodynamic machines – centrifugal pumps and fans – that adjust performance curves for changing speed and impeller diameter. This article focuses on variable speed pumping and the use of affinity laws to predict the performance at speeds other than the published speed. You need accurate source data to get the best results. It is often difficult to read printed graphs to obtain precise values; this article gives a useful method for digitising printed or PDF charts in Excel.

Variable-frequency drives (VFDs) are now ubiquitous for small pumps and are becoming more common for larger ones. You can accurately predict the pump’s performance at varying speeds by applying affinity laws.

The affinity law formulas are simple (see later). Equation 1 relates flow rate to speed and impeller diameter. Equation 2 says that the head is a squared relationship, while in Equation 3 you see that power follows a cubic relationship. If you have a pump or fan curve for one speed and impeller, construct a curve for a different speed and/or diameter using Equations 1 and 2. Figure 1 illustrates how to construct a curve for a reduced speed. The required net positive suction head (NPSHR) also follows Equation 2; although there is a minimum, NPSHR does not trend to zero.