Seepage from Ditches - Solution by Finite Differences

Solutions to steady-state free surface seepage problems from canals of trapezoidal, triangular and rectangular cross sections through homogeneous isotropic and anisotropic porous media to drained layers at finite depths are obtained by methods of finite differences. In the formulation of the problems, the coordinate directions x and y are considered the dependent variables and the velocity potential and the stream function the independent variables. The solutions are obtained by two independent methods. The first method combines solutions for y and x from the plane of the velocity potential and stream function with a solution of the stream function from the physical plane in a cyclic manner. The second method uses complex arithmetic to obtain the solution entirely in the plane of the velocity potential and stream function. A relationship between the seepage quantity and the dimensions of the canal and distance to the drained layer is developed by summarizing solutions obtained for canals of various sizes and shapes.