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On calculation of filtration flows from sprayers of irrigation systems

  • É. N. BereslavskiiEmail author
Article

In the hydrodynamic formulation, consideration is given to plane steady filtration in a homogeneous isotropic ground from sprayers through a soil layer underlain by a highly permeable pressure water-bearing formation in the presence of the ground capillarity and evaporation from the free surface. Filtration is studied by formulating a mixed multiparametric boundary-value problem of the theory of analytical functions, which is solved using the Polubarinova-Kochina method and procedures of conformal mapping of the regions of special kind that are characteristic of underground-hydromechanics problems. On the basis of the model proposed, an algorithm of computation of capillary water spread and filtration flow rate was developed in situations where in the water filtration from sprayers, account is taken of the ground capillarity, evaporation from the free surface, and of the upthrust from the side of the underlying well-permeable formation. With the aid of the exact analytical dependences obtained and of numerical calculations, a hydrodynamic analysis is performed for the structure and characteristic features of the modeled process, and for the influence of all physical parameters of the scheme on the filtration characteristics. Consideration is given to the limiting and particular cases associated with the absence of separate factors characterizing the modeled process, such as the ground capillarity, evaporation from the free surface, and the upthrust from the side of the underlying water-bearing highly permeable layer. Calculated results for filtration from canals with identical filtration characteristics and similar filtration schemes are compared.

Keywords

filtration sprayer groundwater pressure underground water ground capillarity evaporation from the free surface complex flow velocity conformal mappings Polubarinova-Kochina method 

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References

  1. 1.
    N. N. Verigin, Water filtration from an irrigation-system sprayer, Dokl. Akad. Nauk SSSR, 66, No. 4, 589–592 (1949).MathSciNetGoogle Scholar
  2. 2.
    N. N. Verigin, Some cases of rise of groundwater under conditions of general and local enhanced infiltration, Inzh. Sborn., 7, 21–34 (1950).Google Scholar
  3. 3.
    V. I. Aravin and S. N. Numerov, Theory of Motion of Liquids and Gases in an Undeformable Porous Medium [in Russian], Gostekhizdat, Moscow (1953).Google Scholar
  4. 4.
    S. N. Numerov, On one method of solving a filtration problem, Izv. Akad. Nauk SSSR, OTN, No. 4, 133–139 (1954).Google Scholar
  5. 5.
    É. N. Bereslavskii, On the problem of filtration from the irrigation-system sprayer, Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 2, 105–109 (1987).Google Scholar
  6. 6.
    P. Ya. Polubarinova-Kochina, Theory of Motion of Groundwater [in Russian], Gostekhizdat, Moscow (1952); 2nd edn., Nauka, Moscow (1977).Google Scholar
  7. 7.
    É. N. Bereslavskii, On the regime of groundwater during filtration from an irrigation-system sprayer, Prikl. Mekh. Tekh. Fiz., No. 5, 88–91 (1989).Google Scholar
  8. 8.
    É. N. Bereslavskii and V. V. Matveev, Filtration from shallow canals and sprayers, Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 1, 96–102 (1989).Google Scholar
  9. 9.
    Development of Filtration Theory Research in the USSR (1917–1967) [in Russian], Nauka, Moscow (1969).Google Scholar
  10. 10.
    G. K. Mikhailov and V. N. Nikolaevskii, Motion of liquids and gases in porous media, in: Mechanics in the USSR in the Last 50 Years [in Russian], Vol. 2, Nauka, Moscow (1970), pp. 585–648.Google Scholar
  11. 11.
    P. Ya. Kochina, É. N. Bereslavskii, and N. N. Kochina, Analytical Theory of the Fuchs-Class Linear Differential Equations and Some Problems of Underground Hydromechanics, Pt. 1, Preprint No. 567 of the Institute for the Problems of Mechanics, Russian Academy of Sciences, Moscow (1996).Google Scholar
  12. 12.
    É. N. Bereslavskii and P. Ya. Kochina, On the Fuchs-class equations in hydro- and aeromechanics, Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza, No. 5, 3–7 (1992).Google Scholar
  13. 13.
    É. N. Bereslavskii and P. Ya. Kochina, On Fuchs-class differential equations encountered in some problems of the mechanics of liquids and gases, Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza, No. 5, 9–17 (1997).Google Scholar
  14. 14.
    É. N. Bereslavskii, On Fuchs-class differential equations associated with conformal mapping of circular polygons in polar grids, Differ. Uravn., 33, No. 3, 296–301 (1997).MathSciNetGoogle Scholar
  15. 15.
    É. N. Bereslavskii, On closed form integration of some Fuchs-class differential equations encountered in hydroand aeromechanics, Dokl. Ross. Akad. Nauk, 428, No. 4, 439–443 (2009).Google Scholar
  16. 16.
    É. N. Bereslavskii, On closed form integration of some Fuchs-class differential equations associated with conformal mapping of circular pentagons with a cut, Differ. Uravn., 46, No. 4, 459–466 (2010).MathSciNetGoogle Scholar
  17. 17.
    É. N. Bereslavskii, On account for infiltration or evaporation from the free surface by the method of circular polygons, Prikl. Mat. Mekh., 74, Issue 2, 239–251 (2010).MathSciNetGoogle Scholar
  18. 18.
    É. N. Bereslavskii, Mathematical modeling of flows from canals, Inzh.-Fiz. Zh., 84, No. 4, 690–696 (2011).MathSciNetGoogle Scholar
  19. 19.
    W. Koppenfels and F. Stallman, Praxis der konformen Abbildung [Russian translation], IL, Moscow (1963).Google Scholar
  20. 20.
    É. N. Bereslavskii, A case of conformal mapping of circular tetragons by elementary functions, Ukr. Mat. Zh., 37, No. 3, 356–357 (1985).MathSciNetGoogle Scholar
  21. 21.
    É. N. Bereslavskii, On closed form integration of one class of Fuchsian equations and its application, Differ. Uravn., 25, No. 6, 1048–1049 (1989).MathSciNetGoogle Scholar
  22. 22.
    V. V. Golubev, Lectures on the Analytical Theory of Linear Differential Equations [in Russian], Gostekhizdat, Moscow, Leningrad (1950).Google Scholar
  23. 23.
    V. V. Vedernikov, Theory of Filtration and Its Application in the Field of Irrigation and Drainage [in Russian], Gosstroiizdat, Moscow, Leningrad (1939).Google Scholar

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© Springer Science+Business Media, Inc. 2012

Authors and Affiliations

  1. 1.State University of Civil AviationSt. PetersburgRussia

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