Uncertainty analysis for different virtual pump water flow meters

Abstract

The water flow rate through a pump can be calculated using other measured inputs, such as pump head, motor input power, and frequency, along with calibrated characteristic curves. Currently virtual pump flowmeters can be classified into three categories—pump head based, shaft power based, and pump efficiency based—based on which measured inputs and characteristic curves are applied. Thus, different virtual meters may have different flow measurement errors propagated from different measured inputs and curve fittings. This article aims to evaluate the measurement uncertainties of these three virtual meters. First, mathematical models of virtual flow measurement and uncertainty analysis are introduced for three virtual meters. Then through experiments on a 125 m3/h pump, three virtual meters are developed and the uncertainties of the developed virtual meters are evaluated. Finally, the water flow rates measured by three virtual meters are compared with those measured by an ultrasonic flowmeter. Both the uncertainty analysis and flow measurement comparison show that the pump head–based and shaft power–based virtual meters have unacceptable uncertainties, 13 m3/h and 17 m3/h, respectively, at lower frequencies due to the mismatch between the pump speed and motor input frequency. In contrast, the pump efficiency–based virtual meter always remains a robust accuracy with uncertainties less than 1.9 m3/h.