The design of the iso-velocity contour for the flow past the base of a dam with a confining bed

The underground contour of a submerged rectangular dam, the angles of which are rounded off along curves of constant magnitude of the seepage flow velocity is constructed in the case when the water-permeable base is underlain by a confining bed, consisting of one horizontal and two curved sections, which are the iso velocity lines of the seepage flow. The corresponding multiparameter mixed problem in the theory of analytical functions is solved using the Riemann-Schwartz symmetry principle and a semi-inverse version of the velocity hodograph method, first proposed by Polybarinova-Kochina and Kochina. The results of numerical calculations are presented and a hydrodynamic analysis of the effect of the basic physical parameters of the model on the shape and dimensions of the underground contour of the dam and of the horizontal and curved sections of the confining bed is given.