Evaluating the Approximation of the Affinity Laws and Improving the Efficiency Estimate for Variable Speed Pumps

Abstract

Affinity laws relate to the characteristics of pumps operating at different speeds, and in a water distribution context, are usually used to predict the pump curve of variable speed pumps (VSPs). VSPs can adjust the pump curve to meet the network requirements more efficiently with resultant savings of energy. The estimation of the effectiveness of a VSP is based on hydraulic simulations, in which the behavior of VSPs is described using the affinity laws. The affinity laws, however, contain approximations because they do not take into account factors that do not scale with velocity. In particular, the approximation inherent in the affinity law that computes power and efficiency can produce a misleading result, especially for small-size pumps. The research reported in this paper estimates the error in efficiency for a wide range of pump sizes and tests the use of a previously proposed formula as an alternative to the affinity law. Results show that a better estimation can be achieved for the efficiency of small- and medium-size pumps. Moreover the formula can be easily implemented in hydraulic solvers.