Skip to main content
SpringerLink
Log in

On filtration schemes occurring in the problem of flow over a Zhukovskii sheet pile

  • Published:
Journal of Engineering Physics and Thermophysics Aims and scope

Consideration is given to filtration under a Zhukovskii sheet pile through a ground layer underlain by a highly permeable head horizon the left semi-infinite part of whose roof is modeled by an impermeable base. A study is made of the case of flow where the velocity at the end of the sheet pile is equal to infinity and the flow rate takes on extremum values on both water-permeable portions of the boundary of the region of motion. Limiting cases of flow associated with the absence of upthrust and of an impermeable inclusion alike are noted, as is an adjacent scheme due to the absence of the two indicated extremum points. Solutions are given for two schemes of motion in a semi-inverse formulation, with the classical Zhukovskii problem being the limiting case of one scheme. Distinctive features of such models are noted. For investigation of these flows, use is made of a Polubarinova-Kochina method which allows exact analytical representations for motion elements. Results of numerical calculations and the analysis of the influence of all physical factors on filtration characteristics are given.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. É. N. Bereslavskii, On flow over a Zhukovskii sheet pile in an irrigated ground mass, Inzh.-Fiz. Zh., 84, No. 3, 476−484 (2011).

    Google Scholar 

  2. É. N. Bereslavskii, On the regime of groundwater during flow around a Zhukovskii sheet pile, Prikl. Mat. Mekh., 75, Issue 2, 304−313 (2011).

    MathSciNet  Google Scholar 

  3. N. E. Zhukovskii, Seepage of Water through Dams, Collected Works [in Russian], Vol. 7, Gostekhizdat, Moscow (1950), pp. 297−332.

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

  5. 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 

  6. P. Ya. Polubarinova-Kochina (Exec. Ed.), Development of Investigations on the Theory of Filtration in the USSR (1917−1967) [in Russian], Nauka, Moscow (1967).

  7. G. K. Mikhailov and V. N. Nikolaevskii, Motion of Liquids and Gases in Porous Media. Mechanics in the USSR over the Last 50 Years [in Russian], Vol. 2, Nauka, Moscow (1970), pp. 585−648.

  8. P. Ya. Kochina, Hydrodynamics and Filtration Theory, Selected Works [in Russian], Nauka, Moscow (1991).

    Google Scholar 

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

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

  11. É. N. Bereslavskii and P. Ya. Kochina, On the Fuchs class differential equations encountered in some problems of fluid mechanics, Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza, No.5, 9−17 (1997).

  12. É. N. Bereslavskii, About conformal mapping of some circular polygons onto a rectangle, Izv. Vyssh. Uchebn. Zaved., Matematika, No. 5, 3−7 (1980).

  13. É. N. Bereslavskii, On the Fuchs class differential equations related to the conformal mapping of polygons in polar grids, Differents. Uravneniya, 33, No. 3, 296−301 (1997).

    MathSciNet  Google Scholar 

  14. É. N. Bereslavskii, On some Fuchs class differential equations encountered in some problems of fluid mechanics, Differents. Uravneniya, 48, No. 4, 590−594 (2012).

    Google Scholar 

  15. W. Koppenfels and F. Stallmann, Praxis der konformen Abbildung [Russian translation], IL, Moscow (1963).

  16. I. S. Gradshtein and I. M. Ryzhik, Tables of the Integrals of Sums, Series, and Products [in Russian], Nauka, Moscow (1971).

    Google Scholar 

  17. V. V. Golubev, Lecturers on the Analytical Theory of Differential Equations [on Russian], Gostekhizdat, Moscow−Leningrad (1950).

  18. M. A. Lavrentiev and B. V. Shabat, Methods of the Theory of Complex Variable Functions [in Russian], Nauka, Moscow (1965).

    Google Scholar 

  19. É. N. Bereslavskii, On the problem of flow over a Zhukovskii sheet pile in an irrigated ground mass, Inzh.-Fiz. Zh., 85, No. 2, 277−283 (2012).

    MathSciNet  Google Scholar 

  20. A. R. Tsitskishvili, On N. M. Gersevanov’s iteration method, Prikl. Mat. Mekh., 21, Issue 2, 291−296 (1957).

    Google Scholar 

  21. V. N. Émikh, Hydrodynamics of Filtration Flows with Draining [in Russian], Nauka, Novosibirsk (1993).

    Google Scholar 

  22. B. K. Rizenkampf, Groundwater hydraulics, Pt. 3, Uch. Zap. Saratov. Univ., Ser. Fiz.-Mat. Inst., 15, Issue 5, 3−93 (1940).

  23. N. M. Gersevanov, Application of functional analysis in solving the problems of ground water filtration, Izv. Akad. Nauk SSSR, Otd. Tekh. Nauk, No. 7, 73−83 (1943).

  24. N. M. Gersevanov, Iteration Calculus and Its Applications [in Russian], Mashstroiizdat, Moscow (1950).

    Google Scholar 

Download references

Author information

Authors and Affiliations

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

    É. N. Bereslavskii

Authors
  1. É. N. Bereslavskii
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to É. N. Bereslavskii.

Additional information

Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 86, No. 2, pp. 300–309, March–April, 2013.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bereslavskii, É.N. On filtration schemes occurring in the problem of flow over a Zhukovskii sheet pile. J Eng Phys Thermophy 86, 316–326 (2013). https://doi.org/10.1007/s10891-013-0836-9

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10891-013-0836-9

Keywords

Search

Navigation