Developing a new unsteady-state equation for the design of subsurface drainage systems suitable for the Delta region, Egypt

The main goal of this research is to obtain a new unsteady-state equation for the design of subsurface drainage systems that provides a more combatable solution under conditions in the Delta region, Egypt, while simultaneously avoiding all obstacles, difficulties and points of argument in other unsteady-state equations. The point of argument in unsteady-state assumptions is the initial water table shape. Then, the study reached a constant called C-sh, which represents the initial water table shape and was proven to depend on drain depth (d.d.). Moreover, the new equation avoids using the drainable porosity of soil (f), which is the greatest restriction in using unsteady-state equations. The new equation replaces f with another constant called C-s,C- which can be easily determined by using tables or graphs depending on drain depth (d.d.) and hydraulic conductivity (k). Another new important variable is also used in the new equation: the hydraulic head after 6 days of irrigation (h). Using this parameter with the initial water table (h(0)) and the water table after t days (h(t)) ensures more accurate results. Then, the new equation, which can be called the Safaa equation, can result in an optimum solution for the Delta region, Egypt, because it provides spacing between laterals (L), which results in the desired performance with the least cost.