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The following filtration flows with unknown free boundaries are investigated in case of a flow past the Zhukovsky groove in the case when the soil layer is underlain along its entire length with an impermeable base and evaporation from the free surface occurs in case of a flow past the Zhukovsky groove in the case when the underlying layer is a completely well-permeable aquifer and infiltration occurs on the free surface when groundwater moves in a rectangular bridge with a partially impenetrable vertical wall in the presence of evaporation from the free surface when groundwater moves to an imperfect gallery in the presence of evaporation from the free surface. On Accounting for Evaporation or Infiltration Free Surface in some Problems of Filtration Theory International Journal of Advanced Research in Physical Science (IJARPS) Page | 2 Fig1, а. The current picture calculated at ε = 0.6, hc = 0.5, T = 7, S = 3, H = 5. Fig1, б. The current picture calculated at ε = 0.6, T = 7, S = 3, H = 7, H0 = 3 и xC = 100 3. CURRENTS IN A RECTANGULAR JUMPER WITH PARTIALLY IMPENETRABLE VERTICAL WALL AND TO IMPERFECT GALLERY The exact solution of a task on a fluid influx to the imperfect well with the flooded filter (i.e. an axisymmetric task) or the tubular well representing an impenetrable pipe with the filter in some (usually lower) its part is connected with great mathematical difficulties and so far is not found. Therefore in due time as first approximation to a solution of similar tasks by P.Ya. Polubarinova-Kochina, V.G. Pryazhinska, V.A. Postnov and V.N. Emikh [2, 6, 7, 17, 18] considered some corresponding flat task analogs about filtering in a rectangular jumper with partially impenetrable vertical wall and to imperfect gallery. It should be noted that areas of values of complex speed in the specified cases allow to apply by means of inversion at a solution Christoffel-Schwartz's formula. In work the exact analytical solution of a task on a current of subsoil waters in a rectangular jumper with slopes of A0A1 and D0B, width of L located on the impenetrable horizontal basis of length of L is given. Water height is equal in an upper byef to H, lower reach with water level of H2, having partially impenetrable vertical wall CD (screen), adjoins a basis sole. The upper bound of area of the movement is free pover khnost AD which is coming out with which there is a uniform evaporation to intensity ε (fig. 2). In the considered area of complex speed, unlike [2, 6, 7, 17, 18], there are not rectilinear, but circular polygons that does not give the chance to use classical integral of Christoffel-Schwartz. The task solution on a current to the imperfect well formally turns out from a task solution on filtering in a rectangular jumper with partially impenetrable vertical wall in case of its infinite width, i.e. at L = ∞ [19, 20]. 4. TECHNIQUE OF SOLUTIONS For studying of the specified currents in the presence of evaporation or infiltration on a free surface the mixed multiple parameter boundary value problems of the theory of analytic functions which solution is carried out with use of the method of P.Ya. Polubarinova-Kochina [2-7] based on application of the analytical theory of linear differential equations of a class of Fuchs are formulated. And also [21–23] ways of conformal mapping of a special type of circular polygons [24-28] developed for areas which are very typical for tasks of the theory of filtering. Accounting of characteristics of the considered classes of areas of the hodograph of speed allowed to present solutions of tasks in the closed form through elementary functions that does their use the simplest and convenient in practice. On Accounting for Evaporation or Infiltration Free Surface in some Problems of Filtration Theory International Journal of Advanced Research in Physical Science (IJARPS) Page | 3 Fig2. The current picture in a rectangular jumper calculated at ε = 0.5, H = 3, L = 2, H1 = 1, H2 = 1.4.

On Accounting for Evaporation or Infiltration Free Surface in Some Problems of Filtration Theory