Development of a mathematical model to predict clean water head losses in hydrocyclone filters in drip irrigation systems using dimensional analysis

A model was developed using dimensional analysis, to predict head losses in hydrocyclone filters. Different hydrocyclone filters with different specifications were used to measure head losses at different flow rates in the laboratory. The parameters influencing head losses were considered to be the inside diameters of the inlet and outlet pipes, cylindrical section diameter of the filter, apex diameter of the conical part, cylindrical section length of the filter, conical section length of the filter body, length of the outlet (vortex finder) pipe, water velocity in inlet pipe, acceleration of gravity, kinematic viscosity of water. A dimensional analysis was carried out, using Buckinghamʹs pi-theorem. To develop a model, experimental head loss data from 21 filters were considered in the study. The model accounted for 96.7% of the variation in the pressure coefficient. The predicted and the measured head losses were in close agreement with a correlation coefficient of 98.1%. The results showed that the model may be used to determine head losses in hydrocyclone filters with an acceptable accuracy if the variables are within the following ranges: inside diameter of inlet and outlet pipe 0.053–0.154 m; cylindrical section diameter of the filter 0.195–0.46 m; apex diameter of the conical part 0.04–0.06 m; cylindrical section length of the filter 0.16–0.41 m; conical section length of the filter body 0.37–0.955 m; length of the vortex finder pipe 0.155–0.627 m; flow rate 3.7–98.48 m3 h−1; and Reynolds number 18 860–421 065. The performance of the model was compared with models developed for industrial hydrocyclones and the necessary comparisons were established by using statistical test procedures. The model in this study provides better predictions as compared to some other models available in the literature.