Skip to main content
Log in

Construction of the underground contour of a hydraulic structure with constant flow velocity sections

  • Published:
Fluid Dynamics Aims and scope Submit manuscript

Abstract

The underground contour of an embedded rectangular dam, whose corners are rounded in accordance with curves of constant flow velocity and whose water-permeable base is underlain by a confining layer with a curvilinear roof characterized by a constant flow velocity, is constructed. The corresponding boundary value problem is solved by means of the semi-inverse use of the velocity hodograph method. The results of the numerical calculations are given and the effect of the main determining parameters of the model on the shape and dimensions of the underground contour of the dam and the curvilinear confining layer is analyzed. The limiting cases in which the water-permeable base of the dam has an unbounded thickness, namely, a streamlined apron with a horizontal insert and streamlined sheet piling (tooth), are investigated in detail.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. N.N. Pavlovskii, “Theory of Groundwater Movement under Hydraulic Structures and its Main Applications,” in CollectedWorks, Vol. 2 (Izd-vo of the Academy of Sciences of the USSR, Moscow, Leningrad, 1956) [in Russian], 3–352.

    Google Scholar 

  2. A.P. Voshchinin, “Use of Streamlined and Ribbed Underground Contours in the Construction of Hydraulic Structures on a Permeable Base,” Inzh. Sb. 7, 15–20 (1950).

    Google Scholar 

  3. M.T. Nuzhin, “Formulation and Solution of Inverse Problems of Pressurized Flow through a Porous Medium,” Dokl. Akad. Nauk SSSR 96, No. 4, 709–711 (1954).

    MATH  MathSciNet  Google Scholar 

  4. I.N. Kochina and P.Ya. Polubarinova-Kochina, “Use of Smooth Base Contours in Hydraulic Structures,” Prikl. Mat. Mekh. 16, No. 1, 57–66 (1952).

    Google Scholar 

  5. P.Ya. Polubarinova-Kochina, Theory of Groundwater Movements (Gostekhizdat, Moscow, 1952; 2nd edition: Nauka, Moscow, 1977) [in Russian].

    Google Scholar 

  6. G.G. Tumashev and M.T. Nuzhin, Inverse Boundary Value Problems and their Applications (Izd-vo Kazan. University, Kazan’, 1965) [in Russian].

    Google Scholar 

  7. M.T. Nuzhin and N.B. Il’inskii, Methods of Construction of the Underground Contour of Hydraulic Structures. Inverse Boundary Value Problems of the Theory of Flow through a Porous Medium (Izd-vo Kazan. University, Kazan’, 1963) [in Russian].

    Google Scholar 

  8. N.B. Il’inskii, “Development of the Methods of Inverse Boundary Value Problems of the Theory of Flow through a Porous Medium,” in Problems of Theory of Flow through Porous Media and Mechanics of the Process of Enhancing Oil Recovery (Nauka, Moscow, 1987), 98–108.

    Google Scholar 

  9. V.I. Aravin and S.N. Numerov, Percolation and Seepage Calculations for Hydraulic Engineering Structures (Gostekhizdat, Moscow, 1953) [in Russian].

    Google Scholar 

  10. W. von Koppenfels and F. Stallmann, Praxis der Konformen Abbildung (Springer, Berlin etc., 1959; Izd-vo Inostr. Lit., Moscow, 1963).

    MATH  Google Scholar 

  11. É.N. Bereslavskii, “Differential Equations of the Fuchs Class Related with the Conformal Mapping of Circular Polygons in Polar Grids,” Differents. Uravneniya 33,No. 3, 296–301 (1997).

    MathSciNet  Google Scholar 

  12. É.N. Bereslavskii, “ConformalMapping of Certain Circular Polygons onto a Rectangle,” Izv. Vuzov. Matematika, No. 5, 3–7 (1980). 13. É.N. Bereslavskii, “Determination of the Underground Contour of a Subsurface Apron with a Constant Velocity Section in the Presence of Saline BackupWater,” Prikl. Mat. Mekh. 62, No. 1, 169–175 (1998).

    Google Scholar 

  13. I.S. Gradshtein and I.M. Ryzhik, Tables of Integrals, Series, and Products (Academic Press, New York, 1965; Nauka, Moscow, 1971).

    Google Scholar 

  14. É.N. Bereslavskii, “Hydrodynamic Investigation of Certain Groundwater Flows in Coastal Pressurized Aquifers,” Fluid Dynamics 38(3), 433–442 (2003).

    Article  Google Scholar 

Download references

Authors

Additional information

Original Russian Text © E.N. Bereslavskii, 2008, published in Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, 2008, Vol. 43, No. 5, pp. 103–112.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bereslavskii, E.N. Construction of the underground contour of a hydraulic structure with constant flow velocity sections. Fluid Dyn 43, 763–771 (2008). https://doi.org/10.1134/S0015462808050104

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0015462808050104

Keywords

Navigation