Modeling the Movement of Groundwater from the Pits, Surrounded with Tongues of Zhukovsky

Bereslavckii Eduard Naumovich

doi:10.11648/j.ijtam.20170304.11

Abstract

In the hydrodynamic statement the filtration low from ditches, walled tongues of Zhukovsky is considered. The fluid moves through the layer of soil, underlain by a well-permeable pressure aquifer, which is contained waterproof area on the roof. For study the infiltration to the free surface of groundwater is formulated a mixed multi-parameter boundary value problem of the theory of analytic function, which is solved by the Polubarinova-Kochina's method and ways the conformal mapping areas of a special kind, which are characteristic for tasks of an underground hydromechanics.

Highlights

In the hydrodynamic formulation is considered flat established incompressible fluid filtration by Darcy's law in construction ditches fences tongue Zhukovsky through homogeneous and isotropic soil layer underlained by a wellpermeable pressure aquifer on the roof that provides an impermeable land
The use of the SchwarzChristoffel integral does not lead to the goal, as in the areas of integrated flow rate already arise circular polygons, cannot be reduced directly to the straight line. In contrast to these researches below, as a direct continuation and development of the author's previous results [18,19], we study the problem of the flow of fluid from the pits through the dirt array ultimate power, underlain by a well-permeable pressure aquifer that comprising at its waterproof roof portion of infiltration in the presence of the free surface
Within the case L = 0 we focus on the absence of infiltration

Summary

Introduction

In the hydrodynamic formulation is considered flat established incompressible fluid filtration by Darcy's law in construction ditches fences tongue Zhukovsky through homogeneous and isotropic soil layer underlained by a wellpermeable pressure aquifer on the roof that provides an impermeable land. During the study infiltration of the free surface groundwater formulated mixed boundary multiparameter problem of analytic function theory, which is solved by the method Polubarinova-Kochina and methods of conformal mappings of a special type, typical of underground fluid mechanics problems Based on this model, an algorithm of calculation the filtration characteristics in situations when you have to take into account the combined effect of the picture movement of such important factors as the infiltration of the free surface, tight inclusion and backwater from the water well-permeable underlying aquifer. Bereslavckii Eduard Naumovich: Modeling the Movement of Groundwater from the Pits, Surrounded with Tongues of Zhukovsky waterproof horizontal sections (tight turn, impermeable rock), that fundamentally affects the nature of the filtration processes In such situations, the use of the SchwarzChristoffel integral does not lead to the goal, as in the areas of integrated flow rate already arise circular polygons, cannot be reduced directly to the straight line. Highlights were announced earlier [25]

The Basic Model

Construction of the Solution of Boundary Value Problem

Discussion of Results

Limiting Cases

The Case of a Finite Value of Flow Rate at the End of the Dowel

Conclusion