Surface Irrigation Using Kinematic-Wave Method

In the kinematic-wave method, one-dimensional unsteady mathematical model for flow in surface irrigation consists of the equation of continuity for the surface flow, the simplified equation of motion, a uniform-flow formula, for the surface flow, the simplified flow equation for the subsurface flow, the infiltration equation or an empirical formula, and appropriately prescribed initial and boundary conditions. By means of the kinematic-wave method that is only valid for supercritical flow, the model is solved to yield the general solution that depends on the solution form of the cumulative depth of the subsurface flow at the head ditch. A particular solution for a constant infiltration rate reduced from the general solution is shown to be compatible with that obtained from the modified Lewis-Milne equation. The solution has different expressions for laminar and turbulent flows.