A Mathematical Model for Experimental Head-Flow Rate Curve of Partial Emission Pumps

The head-flow rate curve of the partial emission pump is flat and with a sudden drop-off near the maximum flow rate. Thus, it is difficult to fit the experimental head-flow rate curve of the pump by using a polynomial, which is suitable for centrifugal pumps. To tackle this problem, a new mathematical model was put forward in the inspiration of the mathematical model of the equivalent electric circuit of photovoltaic cells/modules. The physics behind the model was described by using flow rate saturation effect in partial emission pumps. The model was implemented in Excel and applied to the experimental head-flow rate data of seven partial emission pumps with different specific speeds in a range of 17-80. The model can produce high-quality curve fitting (coefficient of determination of greater than 0.9), The model is adaptive to the variable experimental head-flow rate data of partial emission pumps due to changes in impeller structure, rotational speed, number of blades and impeller diameter. Further, the model can fit the experimental head-flow rate data with drooping effect at low flow rate in partial emission pumps satisfactorily (coefficient of determination of greater than 0.94). The model potentially can be used in experimental data processing in the pump industry and pump-system modelling for partial emission pumps in future.