Dupuit‐Forchheimer solutions for radial flow with linearly varying hydraulic conductivity or thickness of aquifer

Abstract

This paper presents new analytical solutions for steady state piezometric heads in phreatic and confined aquifers with radial flow. The new solutions utilize two constant head boundaries and a hydraulic conductivity k or thickness of aquifer H that is a linear function of radius r. Previous solutions applied constant k and H, and they were usually based on one constant head boundary, which might be superimposed on a solution that allowed a constant discharge or recharge at the center of the aquifer. The previous solutions may be difficult to apply to real aquifers because constant k and H is usually an oversimplification of nature. The Dupuit‐Forchheimer assumption implies that vertical head gradients are ignored. The magnitude of the error introduced by allowing H = H(r) is evaluated numerically in this paper.