Steady flow from a disc source above a shallow water table

The quasi-linear form of Richards' Equation is used to analyze steady flow from a disc source with uniform flux density in a homogeneous soil with a shallow groundwater table. Additionally, a solution and examples are given for a cylindrical flow region, i.e. of a finite radial extent. Still more general solutions are presented for cylindrical sources, including the limiting cases of point and ring sources, both buried and on the surface. Results for point sources are of particular interest for developing solutions for a wide variety of source geometries. Before the main examples are presented, the solution for the disc source in a semi-infinite domain is compared with that from a disc source with uniform pressure head with the same total flow rate. The results verify that the effect of the source boundary condition is limited to a very small region adjacent to the source and lend credibility to using the solutions interchangeably. For a finite how depth, a shallow groundwater table is shown to dominate the pressure head held. Only near the source do the pressure heads compare to those of a very deep water table. The effect of a limiting finite radius is to make the flow appear more like the one-dimensional case except at the surface itself and close to the disc source. Future applications of the results include modeling preferential flow paths and checking purely numerical solutions of Richards' Equation.