Calculation of filtration from canals and irrigators

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).

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

References

  1. 1.

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

  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).

  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).

  6. 6.

    N. N. Verigin, Water filtration from an irrigation-system canal, Dokl. Akad. Nauk SSSR, 66, No. 4, 589–592 (1949).

    MathSciNet  Google 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).

  9. 9.

    S. N. Numerov, On filtration from canals of derivation hydroelectric power plants and irrigation systems, Izv. VNIIG, No. 34 (1947).

  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).

  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).

  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).

  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).

    Article  Google 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).

  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).

  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).

  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).

    Article  Google 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).

  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).

  21. 21.

    É. N. Bereslavskii, Simulation of filtration flows from canals, Dokl. Ross. Akad. Nauk, 434, No. 4, 472–475 (2010).

    MathSciNet  Google 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.

  23. 23.

    É. N. Bereslavskii, Simulation of filtration flows from canals, Prikl. Mat. Mekh., 75, Issue 4, 563–571 (2011).

  24. 24.

    É. N. Bereslavskii, Mathematical modeling of flows from canals, Inzh.-Fiz. Zh., 84, No. 4, 690–696 (2011).

    MathSciNet  Google 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).

  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).

    MathSciNet  Google 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).

    MathSciNet  Google 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).

    MathSciNet  Google 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 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to É. N. Bereslavskii.

Additional information

Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 85, No. 4, pp. 693–703, July–August, 2012.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Bereslavskii, É.N. Calculation of filtration from canals and irrigators. J Eng Phys Thermophy 85, 752–763 (2012). https://doi.org/10.1007/s10891-012-0711-0

Download citation

Keywords

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