Mathematical Modeling of the Operation of a Hydrophoric Installation

Abstract In this paper, the performance of a pumping system is considered in its operation with a hydrophore vessel connected in parallel. The filling and emptying processes of the hydrophore and their influence on the flow rate to the system and the pump outlet pressure are experimentally investigated. An automated measuring system is used for the measurements of the flow rate and the pressure. That has cyclically recorded the values at equal time intervals. The measurement cycles are synchronized in time and the maximum errors of the measured quantities are known. From the experimental data, empirical relationships are obtained for flow rate and pressure as a function of time, as well as the relationships between the two quantities. The time periods of each of the two processes and the average cycle length are also empirically determined. Confidence intervals of the flow rate are constructed for vessel filling and emptying, respectively, and measurement errors were accounted for. Codes have been created to determine the filling time of a hydrophore vessel and to calculate confidence intervals for this type of pumping systems, thanks to which all calculations have been automated. The described dependencies can be used in planning future experiments.