This paper identifies procedures which can be used to quantify reasonable and useful data arrays for head versus flow, efficiency versus flow, and BHP versus flow of a centrifugal pump for use in hydraulic simulation models. Often during the design phase of a liquid pipeline or distribution system, the designer is able to specify the steady state flowrate and head rise for the pumps in the system. However, for transient analysis the performance of the pump is needed throughout a wider range of flowrates from shutoff to runout conditions (or beyond), wherein both pump head and flow are positive. This paper does not discuss methods for quantifying pump performance in other quadrants of operation, wherein pump head and/or flow are negative. Data arrays for positive pump head, efficiency, and BHP versus flow can be fabricated reasonably well using statistical correlations based on a large collection of such data for various types of centrifugal pumps. This paper provides details of those performance correlations, with discussion of their applicability and limitations. Hydraulic head versus flowrate is characterized by two conjoined parabolic curves having functional continuity and which are based upon statistical data. Efficiency versus flow is characterized by two conjoined power curves having functional continuity and which are based upon statistical data. Brake Horse Power versus flow is determined mathematically from the defined equations which characterize head and efficiency versus flow.
In general, hydraulic simulation software assumes that modeler can characterize pump performance of head versus flow in one of the following ways: A horizontal line. This implies that pump head is constant regardless of flow. This method is limited only to some simple steady state distribution system hydraulics modeling software. An inverted parabola based on user-entered two data points of head versus flow, wherein the first datum occurs at shut-off head, the second datum occurs either at BEP or rated conditions. This method assumes that the slope of the curve is zero at shut-off head. An inverted parabola based on user-entered three data points of head versus flow, wherein the first datum occurs at shut-off head, the second datum usually occurs either at BEP or rated conditions, and the third datum usually occurs at runout. This method permits a non-zero slope at shut-off head. A user-entered array of many data points of head versus flow. This method assumes that the modeler already has a published pump manufacturer's curve in mind, or that the modeler can scale up or down a previously used pump curve so as to fit the intended application. Values of pump performance at positive flowrates other than the user-input data are determined either by linear interpolation or by polynomial spline fit of the input data. In general, hydraulic simulation software tends to make some overly simplifying assumptions about pump efficiency or horsepower, or requires the modeler to characterize efficiency or brake horsepower (BHP) versus flow either from a published pump manufacturer's curve, or assumes the modeler can scale such a curve so as to fit the modeled pump. In the absence of published pump efficiency or BHP data, the task of building data arrays to characterize efficiency or BHP versus flow can be an exercise in guesswork.
