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On the problem of construction of the underground contour of water-development works with portions of constant flow velocity

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Journal of Engineering Physics and Thermophysics Aims and scope

Abstract

The underground contour of a sunk rectangular apron whose angles are rounded off by the curves of constant filtration rate is constructed in the case where the water-permeable base is underlain by a confining layer with a curvilinear roof, characterized by a constant flow velocity, too. The corresponding boundary-value problem is solved by a semiinverse application of the velocity-hodograph method. The cases of the apron with a horizontal insert in flow and the rabbet in flow are studied in detail. The results of numerical calculations are given; the influence of the physical parameters of the model on the shape and dimensions of the underground contour of the dam is analyzed.

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References

  1. N. N. Pavlovskii, The theory of motion of groundwater under water-development works and its main applications, in: Collected Works [in Russian], in 2 vols., Izd. AN SSSR, Moscow-Leningrad, Vol. 2, (1956), pp. 3–352.

    Google Scholar 

  2. A. P. Voshchinin, On application of streamlined and finned underground contours in building water-development works on (a) permeable bases, in: Collected Engineering Papers, 7, 15–20 (1950).

    Google Scholar 

  3. M. T. Nuzhin, On statement and solution of inverse problems of forced filtration, Dokl. Akad. Nauk SSSR, 96, No. 4, 709–711 (1954).

    MATH  MathSciNet  Google Scholar 

  4. I. N. Kochina and P. Ya. Polubarinova-Kochina, On application of smooth contours of the bases of water-development works, Prikl. Mat. Mekh., 16, No. 1, 57–66 (1952).

    Google Scholar 

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

    Google Scholar 

  6. M. T. Nuzhin and G. G. Tumashev, Inverse Boundary-Value Problems and Their Applications [in Russian], Izd. Kazansk. Univ., Kazan' (1965).

    Google Scholar 

  7. M. T. Nuzhin and N. B. Il'inskii, Methods of Construction of the Underground Contour of Water-Development Works. Inverse Boundary-Value Problems of the Theory of Filtration [in Russian], Izd. Kazansk. Univ., Kazan' (1963).

    Google Scholar 

  8. L. A. Aksent'ev, N. B. Il'inskii, M. T. Nuzhin, et al., The theory of inverse boundary-value problems for analytical functions and its applications, in: Adv. Sci. Technol.: Math. Anal., 18, 67–124 (1980).

    MathSciNet  Google Scholar 

  9. N. B. Il'inskii, On development of the methods of inverse boundary-value problems of the theory of filtration, in: Problems of the Theory of Filtration and Mechanics of the Processes of Increase in Petroleum Output [in Russian], Nauka, Moscow (1987), pp. 98–108.

    Google Scholar 

  10. V. I. Aravin and S. N. Numerov, The Theory of Motion of Liquids and Gases in a Nondeformable Porous Medium [in Russian], Gostekhizdat, Moscow (1953).

    Google Scholar 

  11. Development of Investigations of the Theory of Filtration in the USSR (1917–1967), Nauka, Moscow (1969).

  12. G. K. Mikhailov and V. N. Nikolaevskii, Motion of liquids and gases in porous media, in: Mechanics in the USSR over the Past 50 Years [in Russian], Vol. 2, Nauka, Moscow (1970), pp. 585–648.

    Google Scholar 

  13. W. Koppenfels and F. Stallman, Praxis der konformer Abbildung [Russian translation], IL, Moscow (1963).

    Google Scholar 

  14. P. Ya. Kochina, É. N. Bereslavskii, and N. N. Kochina, Analytical Theory of Linear Differential Equations and Some Problems of Underground Hydromechanics, Preprint No. 567 of the Institute of Problems of Mechanics, Russian Academy of Sciences, Pt. 1, Moscow (1996).

  15. É. N. Bereslavskii, On integration of one class of Fuchs equations in closed form and its application, Differents. Uravn., 25, No. 6, 1048–1050 (1989).

    MathSciNet  Google Scholar 

  16. É. N. Bereslavskii, On differential equations of the Fuchsian class connected with conformal mapping of circular polygons in polar grids, Differents. Uravn., 33, No. 3, 296–301 (1997).

    MathSciNet  Google Scholar 

  17. É. N. Bereslavskii and P. Ya. Kochina, On certain equations of the Fuchsian class in hydro-and aeromechanics, Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza, No. 5, 3–7 (1992).

  18. É. N. Bereslavskii and P. Ya. Kochina, On differential equations of the Fuchsian class encountered in some problems of the mechanics of liquids and gases, Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza, No. 5, 9–17 (1997).

  19. A. R. Tsitskishvili, On transformations of certain circular polygons into linear ones, Publications of the Enlarged Sessions of the Seminar of the I. N. Vekua Institute of Applied Mathematics, Academy of Sciences of Georgia, 5, No. 1, 193–196 (1990).

    Google Scholar 

  20. É. N. Bereslavskii, On conformal mapping of certain circular polygons onto a rectangle, Izv. Vyssh. Uchebn. Zaved., Matematika, No. 3, 3–7 (1980).

  21. É. N. Bereslavskii, Construction of the constant-velocity contour of the base of water-development works with filtration of two fluids of different densities, Prikl. Mat. Mekh., 54, No. 2, 342–346 (1990).

    Google Scholar 

  22. É. N. Bereslavskii, Determination of the underground contour of a buried apron with a constant-velocity portion in the presence of saline backwater, Prikl. Mat. Mekh., 62, No. 1, 169–175 (1998).

    MathSciNet  Google Scholar 

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  1. St. Petersburg State University of Civil Aviation, 38 Pilotov Str., St. Petersburg, 196210, Russia

    É. N. Bereslavskii

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  1. É. N. Bereslavskii
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Correspondence to É. N. Bereslavskii.

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Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 81, No. 5, pp. 826–833, September–October, 2008.

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Bereslavskii, É.N. On the problem of construction of the underground contour of water-development works with portions of constant flow velocity. J Eng Phys Thermophy 81, 862–869 (2008). https://doi.org/10.1007/s10891-009-0129-5

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