A computationally-efficient finite element method for the hydraulic analysis and design of subsurface drip irrigation subunits

Abstract

A finite element model was developed for the hydraulic design of subsurface drip irrigation subunits. The governing differential equation for steady-state water flow in a multi-outlet pipeline was derived according to the energy and mass conservation equations and was discretized using the Galerkin method. An equation system containing unknown hydraulic heads was constructed and solved using direct stiffness algorithm and Gaussian elimination. The local head loss from the emitter was calculated as a fraction of the kinetic head. The emitter flow rate and its variation were evaluated using an analytical expression of positive soil water pressure and a log transformation of saturated hydraulic conductivity. The model adopted a virtual emitter concept, which allowed for rapid convergence on an ordinary computer. The finite element formulation made the model capable of analyzing both branched and looped pipe network systems. A MATLAB software script was developed, and the hydraulic performance of subsurface drip irrigation subunits was analyzed. The results indicate that a higher number of elements discretized in a pipe led to a higher accuracy of the model, with 20 elements being sufficient. The subsurface drip irrigation subunit can be recognized as an integrated water energy dissipation system. The average value and uniformity of emitter flow rate were determined by the pipe system and soil hydraulic properties. The designed maximum lateral length of a drip and a subsurface drip irrigation subunit was different. In the presented design example, that difference was determined by the emitter nominal flow rate and variation of the soil saturated hydraulic conductivity.