Modeling of the base of a hydraulic structure with constant flow velocity sections and a curvilinear confining layer

We construct the underground contour of an embedded rectangular dam, whose corners are rounded by curves of constant flow velocity. We consider the case of a water-permeable base underlain by a curvilinear confining layer with a horizontal part, whereas the remainder parts of the layer are characterized by a constant flow velocity. We obtain an analytical solution to the corresponding mixed problem of the theory of analytic functions, we present results of numerical computations and consider the limiting case studied earlier by P. Ya. Polubarinova-Kochina and I. N. Kochina.