Development of a mathematical model to predict head losses from disc filters in drip irrigation systems using dimensional analysis

A model was developed using dimensional analysis to predict head losses in disc filters. Three different filter designs, each with four different inlet and outlet pipe diameters, 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, the inside diameter of the filter body, the inflow and outflow area where the inlet and the outlet pipes intersect with the body of the filter, the, effective length of filter disc group, the outside and inside diameter of the filter disc, the water velocity in the inlet pipe and the kinematic viscosity of water. A dimensional analysis was carried out using Buckingham's pi-theorem. To develop the model, experimental head loss data from 12 filters were considered. The model accounted for 90.18% of the variation in the pressure coefficient. A comparison between the predicted and the measured head losses was in close agreement with a correlation coefficient of 99.5%. The results showed that the model may be used to determine head losses in disc filters with an acceptable accuracy if the variables are within the following ranges; inside diameters of inlet and outlet pipe 52.5–102.3 mm; inside diameter of filter body 155–210 mm; effective length of disc group 231–545 mm, inside diameter of filter disc 105–128 mm; outside diameter of filter disc 129–164 mm; inflow area where the inlet pipe intersects with the body of the filter 2240–16430 mm2; outflow area where the outlet pipe intersects with the body of the filter 2160–9480 mm2; flow rate 4.50–73.43 m3h−1; and Reynolds number 19,005–361,310.