The form of an irrigation system is determined from the condition of an extremal value of the backwater or water-table lowering subject to isoperimetric constraints. The unknown functionals and equations of the extremals are written down in explicit form on the basis of the method of Lagrangian multipliers. Seepage in the region of irrigation systems can have both a negative effect on the adjacent territory (water-table elevation, swamping, salination near large canals and reservoirs) and improve the water regime of the soil (regulation of the drying norms by drainage). From the practical point of view, it is important to know how to find the distortions of the natural level of ground water introduced by such systems, and also to determine the influence of the resulting flows on artificial (foundations, screens to prevent seepage) and natural (troughs, slopes) objects. For known hydrogeological conditions, regimes of pressure variation, and disposition of the supply and discharge regions, these problems can be solved either in the framework of a hydraulic  or hydrodynamic  flow model. In this paper, a hydrodynamic model is used to estimate the raising of the ground-water level due to seepage from a channel, its lowering by a drain, and the seepage pressure force on the foundation near a reservoir. It is important that these estimates are obtained by solving problems of constructive type, i.e., problems in which the arrangement of the system (supply, water receiving, or topping-up contour) is not specified in advance but is found as an extremal of an isoperimetric problem.
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