Unsteady Flow to Bottom Drain in Bounded Aquifer

The problem of transient seepage toward a drain at the bottom of a homogeneous, isotropic aquifer is presented. The dependent variables are the position of the free surface, the flow rate, and the pore pressure distribution around the drain, and these are determined as functions of time for various depths of drainage and drain sizes; the characteristics of the aquifer are specified in terms of its coefficient of permeability and its effective porosity. The mathematical statement of this problem yields to a time-dependent potential field within a strip domain bounded by the impervious bottom, the moving free surface, and a small semicircular contour representing the drain. To overcome the difficulty of a moving boundary, a conformal mapping technique is used to transform the problem into a new plane in which the free surface remains straight and fixed. The solution of the problem is found to the third order of time, and an upper bound is given to limit the range within which it is valid.