Steady Infiltration from a Shallow Circular Pond

TLDR

Steady infiltration from a shallow circular pond on a semi‑infinite porous medium is analyzed using J. R. Philip’s linearization method.

Abstract

Steady infiltration from a shallow, circular, inundated area on the horizontal surface of a semi‐infinite porous medium is treated by a method of linearization proposed by J. R. Philip. Using this method, Philip retains most of the properties of the nonlinear system but reduces the differential equation to a linear type governing steady diffusion in a steady uniform flow. On the surface of the medium, the boundary conditions are of mixed type, although linear. These conditions are reduced to a system of dual integral equations solved by a modification of Tranter's method. Expressions for the distributions of vertical flux density, moisture content, and Stokes' stream function are derived, and numerical values of the last two quantities are illustrated graphically. It is found that the total flux depends almost linearly upon a parameter α, defined as the logarithmic derivative of the hydraulic conductivity with respect to capillary potential. Curves of mean flux over various radii (fractions of the total source radius) for various values of α indicate the importance of the guard ring in infiltrometer design.