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Russian Academy of Sciences
in January 1936
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IssuesArchive of Issues2010-2pp.171-180

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Total articles in the database: 1813
In Russian (): 1014
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E.N. Bereslavskii, "Investigation of the effect of seepage or evaporation from a free surface by the method of circular polygons," J. Appl. Math. Mech. 74 (2), 171-180 (2010)
Year 2010 Volume 74 Issue 2 Pages 171-180
Title Investigation of the effect of seepage or evaporation from a free surface by the method of circular polygons
Author(s) E.N. Bereslavskii (St Petersburg, Russia,
Abstract It is proposed to use a technique developed for polygons in polar nets to integrate equations of the Fuchs class that arise when solving a wide range of problems of plane steady seepage flow using the Polubarinova-Kochina method, based on the use of the analytical theory of linear differential equations. It is shown that, for a large class of pentagons in domains where the flows,which are very characteristic of seepage problems when there is infiltration or evaporation from the free surface, have a complex velocity, the solution of the problem of determining the unknown parameters which appear in the conformal mapping can be completed. In this case, the mapping is carried out in closed form in terms of elementary functions and it is simple and convenient for subsequent application. The results obtained are used to solve the problem of seepage from a channel, taking account of the capillarity of the ground when there is evaporation from the free surface. The results of numerical calculations are presented and a hydrodynamic analysis of the effect of the basic physical parameters of the model on the dimensions of the saturation zone is given.
Received 15 June 2009
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