Abstract
We construct the underground contour of an embedded rectangular dam, whose corners are rounded by curves of constant flow velocity. We consider the case of a water-permeable base underlain by a curvilinear confining layer with a horizontal part, whereas the remainder parts of the layer are characterized by a constant flow velocity. We obtain an analytical solution to the corresponding mixed problem of the theory of analytic functions, we present results of numerical computations and consider the limiting case studied earlier by P. Ya. Polubarinova-Kochina and I. N. Kochina.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
I. N. Kochina and P. Ya. Polubarinova-Kochina, “On Application of Smooth Contours of Hydraulic Structure Bases,” Prikl. Mat. Mekh. 16(1), 55–66 (1952).
P. Ya. Polubarinova-Kochina, Theory of ground water movement (Gostekhizdat, Moscow, 1977) [in Russian].
G. G. Tumashev and M. T. Nuzhin, Inverse Boundary-Value Problems and Their Applications (Kazansk. Gos. Univ., Kazan, 1965) [in Russian]
L. A. Aksent’ev, N. B. Il’inskii, M. T. Nuzhin, R. B. Salimov, and G. G. Tumashev, “Theory of Inverse Boundary-Value Problems for Analytic Functions and Its Applications,” Itogi Nauki i Tekhniki, Matem. Analiz 18, 67–124 (1980).
W. Koppenfels and F. Stallmann Practice of Conformal Mappings (Springer-Verlag, Berlin-Gottingen-Heidelberg, 1963; Inostr. Lit.,Moscow, 1963).
V. I. Aravin and S. N. Numerov, Theory of Fluid Flow in Undeformable Porous Media (Pergamon Press, 1959; Gostekhizdat,Moscow, 1959).
E. N. Bereslavskii, “On Differential Equations of the Fuchs Class Connected with Conformal Mappings of Circular Polygons in Polar Grids,” Differents. Uravneniya 33(3), 296–301 (1997).
E. N. Bereslavskii, “Conformal Mapping of Certain Circular Polygons Onto Rectangles,” Izv. Vyssh. Uchebn. Zaved. Mat., No. 5, 3–7 (1980). [SovietMathematics (Iz. VUZ) 24 (5), 1–5 (1980)].
I. S. Gradshtein and I. M. Ryzhik, Tables of Integrals, Sums, Series, and Products (Nauka, Moscow, 1971) [in Russian].
E. N. Bereslavskii, “Finding the Underground Contour of an Embedded Apron with a Constant Flow Velocity Section and Saline Water, Underlying the Dam Base,” Prikl. Mat. Mekh. 62(1), 169–175 (1988).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © E.N. Bereslavskii, L.A. Aleksandrova, 2009, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2009, No. 3, pp. 73–79.
About this article
Cite this article
Bereslavskii, E.N., Aleksandrova, L.A. Modeling of the base of a hydraulic structure with constant flow velocity sections and a curvilinear confining layer. Russ Math. 53, 61–66 (2009). https://doi.org/10.3103/S1066369X09030050
Received:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S1066369X09030050