2 ; 1 ; in Month : January (2021) Article No : sgrj-v2-1004
Bereslavskii Eduard Naumovich

Abstract
Within the framework of planar steady-state filtration of incompressible fluid according to Darcy's law, an exact analytical solution of the problem of flow in a rectangular cofferdam with a screen in the presence of evaporation from the free surface of groundwater is given. The limiting cases of the considered motion - filtration in unconfined reservoir to imperfect gallery, as well as the flow in the absence of evaporation - are noted. Introduction. The solution of the problem of fluid inflow to an imperfect well with a flooded filter (i.e. axisymmetric problem) in the exact hydrodynamic formulation is associated with great mathematical difficulties (especially for flows with a free surface) and is not available so far [1-6] (numerous numerical and approximate solutions are not considered here). Therefore, as a first approximation to the solution of this problem, its flat analogues-problems about fluid flow to a rectangular cofferdam with a screen and to an imperfect rectilinear gallery-were considered [1, 5-8], which give a certain qualitative insight into the possible dependence of filtration characteristics on the degree of well imperfection. Exact analytical solution of the problem of groundwater movement in unconfined reservoir to imperfect gallery in presence of evaporation from free surface is given in work [9]. As well as an approximate solution of the problem in the case when the flow area on the left is limited by some equipotential defined from the solution. It is shown that the flow pattern near the impermeable screen significantly depends not only on the imperfection of the gallery, but also on the presence of evaporation, which strongly affects the flow rate of the gallery and the ordinate of the exit point of the depression curve on the impermeable wall.

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