Steady, two-dimensional flow of ground water to a trench

The problem under consideration is a steady ground water inflow to a single trench which drains a water-bearing layer of infinite extent. The equipotential corresponding to the trench outline is determined from the solution for extremum problems. The isoperimetric constraints selected for solution of these problems include cross-sectional area, seepage flow rate and size of a region with a guaranteed head loss. The equations for the required extremals and variable functions are written explicitly in terms of the solution for the Dirichlet problem.