Unsteady flow in unsaturated soils from a cylindrical source of finite radius

A solution to the two-dimensional diffusion equation for unsteady and unsaturated flow in soils has been obtained. The physical problem is that of flow from a cylindrical source of finite radius and infinite length. Neglecting gravity, the diffusion equation is reduced to a simple form which can be transformed to a nonlinear ordinary differential equation. This transformation is achieved after substituting an empirical relation for the diffusivity of the soil. This ordinary differential equation is then solved by numerical techniques. Two soils, Yolo light clay and Pachappa loam, have been used for examples. Infiltration rates have been computed in each case; these are found to be almost constant for this problem. A computer model in extended Algol language has been developed.