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.
Highlights
The solution of the problem of fluid inflow to an imperfect well with a flooded filter in the exact hydrodynamic formulation, is associated with great mathematical difficulties and so far does not exist [1,2,3,4,5,6]
The task is to determine the position of the free surface AD and to find the ordinate H0 of the exit point of the depression curve on the screen, as well as the filtration flow rate Q
We introduce an auxiliary canonical variable and functions: z( ) conformally mapping the upper half-plane >0 to the flow region z under the correspondence of points D = 0, E = e, A = 1, A1 = a1, B = b, (a1, b are unknown affixes of points A1 and B in the plane ), C = ∞, and functions d / d and dz / d
Summary
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 so far does not exist [1,2,3,4,5,6] (numerous numerical and approximate solutions are not considered here). The task is to determine the position of the free surface AD and to find the ordinate H0 of the exit point of the depression curve on the screen, as well as the filtration flow rate Q.
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