A Standardized Treatment Model for Head Loss of Farmland Filters Based on Interaction Factors

A head loss model for pressureless mesh filters used in farmland irrigation was developed by integrating the four basic test factors: irrigation flow, filter cartridge speed, self-cleaning flow, and initial sand content. The model’s coefficient of determination was found to be 98.61%. Among the basic factors, the total irrigation flow accounted for only 17.20% of the relatively small self-cleaning flow. The contribution of initial sand content was found to be the smallest, with a coefficient of only 0.0166. Furthermore, the contribution rate of the flow term was significantly higher than that of the initial sand content, with a value of 159.73%. In terms of quadratic interaction, the difference between the interaction term of flushing flow and filter cartridge speed, and the interaction term of filter cartridge speed and self-cleaning flow was 38.42%. On the other hand, the difference within this level for the interaction term between initial sand content and filter cartridge speed, as well as the interaction term between irrigation flow and self-cleaning flow, was 2.82%. Finally, through joint optimization of the response surface and model, the optimal values for the irrigation flow rate, filter cartridge speed, self-cleaning flow rate, and initial sand content were determined to be 121.687 m3·h−1, 1.331 r·min−1, 19.980 m3·h−1, and 0.261 g·L−1; the measured minimum head loss was found to be 21.671 kPa. These research findings can serve as a reference for enhancing the design of farmland filters and optimizing irrigation systems.