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Solutions to s.teady-state free surface seepage from axisymmetric ponds through homogeneous and nonhomogeneous porous mediums to a drained layer at a finite depth are obtained by finite difference methods. In the formulation of the boundary value problems, the magnitudes of the radial and axial coordinates are considered dependent variables in the plane defined by the potential function and Stokes' stream function. Example solutions are given for seepage through (1) a homogeneous porous medium; (2) a nonhomogeneous porous medium in which the permeability decreases with depth; and (3) a nonhomogeneous porous medium in which the permeability increases with depth. The methods and techniques employed are equally applicable to other three-dimensional seepage and potential fluid flow problems with axial symmetry and free surfaces. The essential differences in the formulation and solution to other problems will be the boundary conditions. (Key words: Porous mediums; seepage) ington, 1953. Taylor, A., Advanced Calculus, Ginn and Company, New York, 1955.

The problem of flow from a large reservoir through a circular orifice is formulated by considering the velocity potential and Stokes's stream function as the independent variables and the radial and axial dimensions as the dependent variables, and a finite difference solution is obtained to the resulting boundary-value problem. This inverse formulation has the advantage over a finite difference solution in the physical plane that the region of flow is rectangular and consequently well adapted for minimum logic in programming a digital computer. The inverse finite difference solution is more readily obtained than a comparable solution in the physical plane, even though the inverse partial differential equation and associated boundary conditions are non-linear. The results from the inverse finite difference solution are in close agreement with other most recent results from approximate solutions to this problem.The inverse method of solution is applicable to other free streamline as well as confined axisymmetric potential flow problems. The essential difference in other problems will be in the boundary conditions.Keywords: Orifice, Finite Differences, Non-linear Partial Differential Equation, Potential Flow.