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Calculation of filtration from canals and irrigators

  • É. N. BereslavskiiEmail author
Article

Some schemes of the steady plane filtration from canals and irrigators through a soil layer underlain by a pressure highly permeable water-bearing horizon or an impermeable base in the presence of the ground capillary and evaporation from the free surface of the underground water were considered. The filtration water flows in these schemes were investigated by solving the mixed multiparametric boundary-value problems of the theory of analytical functions with the use of the Polubarinova-Kochina method. On the basis of the models proposed, algorithms have been developed for calculating the sizes of the saturation zone and the rate of the filtration water flow in a canal and an irrigator with account for the ground capillary, the evaporation from the free surface of the underground water, the water depth in the canal, and the upthrust formed by the water in the underlying well-permeable horizon or the water on the impermeable base. The results of calculations carried out for schemes with identical filtration parameters were compared depending on the shape of the bed of the water source (a canal or an irrigator) and on the type of the soil-layer base (a well-permeable waterbearing horizon or a confining layer).

Keywords

filtration canal irrigator ground water underground water ground capillarity evaporation upthrust complex flow velocity conformal mapping Polubarinova-Kochina method 

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References

  1. 1.
    P. Ya. Polubarinova-Kochina, Theory of Motion of Ground Waters [in Russian], Gostekhizdat, Moscow (1952); 2nd edn., Nauka, Moscow (1977).Google Scholar
  2. 2.
    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
  3. 3.
    Development of Investigations into the Theory of Filtration in the USSR (1917–1967) [in Russian], Nauka, Moscow (1969).Google Scholar
  4. 4.
    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
  5. 5.
    B. K. Rizenkampf, Hydraulics of ground waters, in: Uch. Zap. Saratovsk. Univ., Ser. Gidravlika, 15, No. 5, 3–93 (1940).Google Scholar
  6. 6.
    N. N. Verigin, Water filtration from an irrigation-system canal, Dokl. Akad. Nauk SSSR, 66, No. 4, 589–592 (1949).MathSciNetGoogle Scholar
  7. 7.
    N. N. Verigin, Some cases of groundwater lift under the conditions of general and local enhanced infiltration, in: Inzh. Sb., 7, 21–34 (1950).Google Scholar
  8. 8.
    S. N. Numerov, A method of solving filtration problems, Izv. Akad. Nauk SSSR, Otd. Tekh. Nauk, No. 4, 133–139 (1954).Google Scholar
  9. 9.
    S. N. Numerov, On filtration from canals of derivation hydroelectric power plants and irrigation systems, Izv. VNIIG, No. 34 (1947).Google Scholar
  10. 10.
    V. A. Vasil’ev, Filtration from a canal with a small water depth and a capillarity, in: Proc. Central Asiatic Univ., 83, No. 14, 43–57 (1958).Google Scholar
  11. 11.
    V. N. Émikh, On the regime of ground waters in an irrigated soil layer with an underlying pressure highly permeable water-bearing level, Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 2, 168–174 (1979).Google Scholar
  12. 12.
    É. N. Bereslavskii and V. V. Matveev, Filtration from canals with a small water depth and irregators, Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 1, 96–102 (1989).Google Scholar
  13. 13.
    É. N. Bereslavskii, On the regime of groundwater in the filtration from an irrigation-system canal, Prikl. Mekh. Tekh. Fiz., No. 5, 88–91 (1989).Google Scholar
  14. 14.
    A. R. Kasimov (Kacimov) and Yu. V. Obnosov, Strip-focused phreatic surface flow driven by evaporation: analytical solution by the Riesenkamph function, Adv. Water Resour., 29, 1565–1571 (2006).CrossRefGoogle Scholar
  15. 15.
    V. A. Baron, Filtration from a canal with a small water depth in the presence of a well-permeable layer with a finite depth and infiltration, Prikl. Mekh. Tekh. Fiz., No. 1, 101–105 (1961).Google Scholar
  16. 16.
    É. N. Bereslavskii and L. A. Panasenko, On determination of the sizes of the saturation zone in the filtration from a canal with a small water depth, Prikl. Mekh. Tekh. Fiz., No. 5, 92–94 (1981).Google Scholar
  17. 17.
    É. N. Bereslavskii, On the problem of filtration from an irrigation-system canal, Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 2, 105–109 (1987).Google Scholar
  18. 18.
    A. R. Kasimov (Kacimov), Yu. V. Obnosov, and J. Perret, Phreatic surface flow from a near reservoir saturated tongue, J. Hydrol., 296, 271–281 (2004).CrossRefGoogle Scholar
  19. 19.
    N. B. Il’inskii and A. R. Kasimov, The inverse problem on filtration from a canal in the presence of an upthrust, in: Proc. of a Seminar on Boundary-Value Problems, Issue 20, Izd. Kazansk. Univ., 104–115 (1983).Google Scholar
  20. 20.
    A. R. Kasimov, Filtration optimization of the shape of an earth canal with account for the capillarity, in: Computational and Applied Mathematics, Issue 61, 70–74, Izd. Kievsk. Univ., Kiev (1987).Google Scholar
  21. 21.
    É. N. Bereslavskii, Simulation of filtration flows from canals, Dokl. Ross. Akad. Nauk, 434, No. 4, 472–475 (2010).MathSciNetGoogle Scholar
  22. 22.
    É. N. Bereslavskii, L. A. Aleksandrova, N. V. Zakharenkova, and E. V. Pesterev, Simulation of filtration flows with free boundaries in underground hydromechanics, in: Abstracts of papers of the 16th School-Seminar under the direction of Academician of the Russian Academy of Sciences G. G. Chornyi "Today’s Problems of Aerohydrodynamics," Izd. Moskovsk. Univ., Moscow (2011), pp. 17–18.Google Scholar
  23. 23.
    É. N. Bereslavskii, Simulation of filtration flows from canals, Prikl. Mat. Mekh., 75, Issue 4, 563–571 (2011).Google Scholar
  24. 24.
    É. N. Bereslavskii, Mathematical modeling of flows from canals, Inzh.-Fiz. Zh., 84, No. 4, 690–696 (2011).MathSciNetGoogle Scholar
  25. 25.
    É. N. Bereslavskii, L. A. Aleksandrova, N. V. Zakharenkova, and E. V. Pesterev, Mathematical simulation of filtration flows with unknown boundaries in underground hydromechanics, in: 10th All-Russia Congress on Fundamental Problems of the Theoretical and Applied Mechanics, Bull. of the N. I. Lobachevskii Nizhnii-Novgorod University, No. 4 (3), 644–646 (2011).Google Scholar
  26. 26.
    É. N. Bereslavskii, On calculation of filtration flows from sprayers of irrigation systems, Inzh.-Fiz. Zh., 85, No. 3, 482–488 (2012).Google Scholar
  27. 27.
    É. N. Bereslavskii, On the Fuchs-class differential equations for conformal mapping of circular polygons in polar grids, Differ. Uravn., 33, No. 3, 296–301 (1997).MathSciNetGoogle Scholar
  28. 28.
    É. N. Bereslavskii, On closed-form integration of some Fuchs-class differential equations used in hydro- and aeromechanics, Dokl. Ross. Akad. Nauk, 428, No. 4, 439–443 (2009).Google Scholar
  29. 29.
    É. N. Bereslavskii, On closed-form integration of some Fuchs-class differential equations for conformal mapping of circular pentagons with a cut, Differ. Uravn., 46, No. 4, 459–466 (2010).MathSciNetGoogle Scholar
  30. 30.
    É. N. Bereslavskii, On consideration of infiltration or evaporation from the free surface by the method of circular polygons, Prikl. Mat. Mekh., 74, Issue 2, 239–251 (2010).MathSciNetGoogle Scholar
  31. 31.
    É. N. Bereslavskii and N. V. Zakharenkova, Influence of the ground capillarity and of evaporation from the free groundwater surface on filtration from canals, Inzh.-Fiz. Zh., 83, No. 3, 470–477 (2010).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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