The flow of liquid from the sprinklers

È. N. Bereslavskii

Matematičeskoe modelirovanie, Tome 24 (2012) no. 2, pp. 99-108.

Résumé

In the hydrodynamic formulation is considered a plane steady seepage in a homogeneous isotropic soil of irrigation canals through the soil layer with the underlying strongly permeable confined aquifer in the presence of capillarity of the soil and evaporation from the free surface. For its study formulated a multiparametric mixed boundary value problem of analytic function theory, which is solved by applying the method Polubarinova-Kochina and methods of conformal mapping of regions of a special kind of typical problems of underground hydrodynamics. On the basis of this model, the algorithm of the calculation of the capillary spreading of water and filtration flow rate in situations, when filtering water from canals into account soil capillarity, evaporation from the free surface of groundwater, as well as backwater from the waters of the underlying well-permeable layer. With the help of obtained exact analytical relationships and numerical calculations carried out a hydrodynamic analysis of the structure and characteristics of the simulated process, as well as the influence of all physical parameters of the scheme on the filtration characteristics. The limiting and special cases related to the absence of one or two of the three factors that characterize the simulated process: the capillarity of soil evaporation from the free surface, as well as backwater from the waters of the underlying aquifer strongly permeable layer. Finally, the results are compared with identical filter characteristics with a similar scheme for filtering of the channels.

Détail

Mots-clés : filtration
Keywords: irrigation, ground water, ground water pressure, capillarity of soil evaporation from the free surface, the complex velocity of flow, conformal mapping method Polubarinova-Cochina.

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