Abstract
We consider a plane steady-state filtration in a rectangular bridge with a partially impermeable vertical wall in the presence of evaporation from a free surface of groundwater. To study the effect of evaporation, a mixed multiparametric boundary-value problem of the theory of analytic functions is formulated and using the method of P. Y. Polubarinova-Kochina. Based on the proposed model, an algorithm is developed to calculate the dependence of efficiency and productivity of hydrodynamic analysis.
Highlights
As it is known [1,2,3,4,5,6], the exact solution of tasks on inflow of liquid to an imperfect well with the flooded filter or the tubular well representing an impenetrable pipe with the filter in its some part is connected with great mathematical difficulties and so far isn't found
It should be noted that areas of complex speed of the specified cases allow to apply by means of inversion at the decision Christoffel-Schwartz's formula
In work [9] it is shown that the current picture near the impenetrable screen significantly depends on imperfection of gallery, and on evaporation existence that is strongly reflected in an expense of gallery and ordinate of a point of an exit of a curve depression to an impenetrable wall
Summary
As it is known [1,2,3,4,5,6], the exact solution of tasks on inflow of liquid to an imperfect well with the flooded filter (i.e. an axisymmetric task) or the tubular well representing an impenetrable pipe with the filter in its some part is connected with great mathematical difficulties and so far isn't found. In the real work the exact analytical solution of a task on a current of ground waters through a rectangular crossing point with partially impenetrable vertical wall in the presence of evaporation from a free surface of ground waters is given. In this case in the field of complex speed, unlike [1, 4, 6,7,8]there are not rectilinear, but circular polygons that doesn't give the chance to use classical integral of Christoffel-Schwartz. The received results, at least, qualitatively can be postponed for a case of tubular wells
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