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Boussinesq equation for flow in an aquifer with time dependent porosity

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Języki publikacji
EN
Abstrakty
EN
A problem of the Boussinesq type for flow of incompressible fluid through a medium with the porosity being a given function of time is studied. At first, from the continuity equation the Dupuit relation for the fluid velocity in the considered medium is found. Next the Boussinesq equation is derived for the medium. This equation, if written for quantity H = h/ and not for the hydraulic head h, has a form of the classical Boussinesq equation, with the coefficient not constant but dependent on time, however. An example of the solution of the modified Boussinesq equation is also given.
Słowa kluczowe
Rocznik
Strony
165--170
Opis fizyczny
Bibliogr. 25 poz., rys.
Twórcy
autor
  • Institute of Fundamental Technological Research, Polish Academy of Sciences, 5B Pawińskiego St., 02-106 Warszawa, Poland, rwojnar@ippt.gov.pl
Bibliografia
  • [1] http://en.wikipedia.org/wiki/Rannoch Moor, 2009.
  • [2] J. Depuit, ´Etudes Th´eoretiques et Pratiques sur le Mouvement des Eaux dans les Canaux D´ecouverts et a Travers les Terrains Permeables, Dunod, Paris, 1863.
  • [3] W.H. Hager, “Jules Dupuit – eminent hydraulic engineer”, J. Hydraulic Engineering 130 (9), 843–848 (2004).
  • [4] J. Boussinesq, “Recherches th´eoriques sur ´ecoulement des nappes d’eau infiltr´ees dans le sol”, J. de math´ematiques pures et appliquees 5 (X(1) 5–78), 363–394 (1904).
  • [5] V.V. Vedernikov, “A physical picture of free seepage”, Comptes Rendus de l’Acad´emie de Sciences de l’URSS 55 (3), 199–202 (1947).
  • [6] P.Y. Polubarinova-Kochina, Theory of Ground Water Movement, Princeton University Press, Princeton, New Jersey, 1962.
  • [7] G.I. Barenblatt, V.M. Entov and V.M. Ryzhik, Theory of Fluid Flows Through Natural Rocks, Kluver Academic Publishers, London, 1984.
  • [8] Y.B. Zeldovich and A.S. Kompaneets, “The theory of heat propagation in the case where conductivity depends on temperature”, in: Collection of Papers Celebrating the Seventieth Birthday of Academician A.F. Ioffe, pp. 61–71, ed. P.I. Lukirskii, Izdat. Akad. Nauk SSSR, Moskva, 1950, (in Russian).
  • [9] H. Darcy, Les Fontaines Publiques de la Ville de Dijon, Dalmont, Paris, 1856.
  • [10] J.J. Telega and R. Wojnar, “Electrokinetics in random piezoelectric porous media”, Bull. Pol. Ac.: Tech. 55 (1), 125–128 (2007).
  • [11] P. Vergili Maronis, Bucolica Georgica Aeneis, Otto G¨uthling, B.G. Teubner, Lipsiae, 1894-1896.
  • [12] M.S. Seyfried and M.D. Murdock, “Use of air permeability to estimate infiltrability of frozen soil”, J. Hydrology 202 (1–4), 95–107 (1997).
  • [13] W. Derski, R. Izbicki, I. Kisiel, and Z. Mróz, Mechanics of Rocks and Soils, PWN, Warszawa, 1982, (in Polish).
  • [14] S.T. Willatt, “Changes in water content in and under frozen soil in Iowa”, Geoderma 22 (4), 323–331 (1979).
  • [15] Soil compaction: en.wikipedia.org/wiki/Soil compaction, 2009.
  • [16] Consolidation (soil): en.wikipedia.org/wiki/Consolidation (soil), 2010.
  • [17] W. Derski, “A method of solving of the system of equations of consolidation theory”, Bull. Pol. Ac.: Tech. XII (10), 489–493 (1964).
  • [18] W. Derski, “Equations of the consolidation theory for the case of a source of fluid”, Bull. Pol. Ac.: Tech. XIII (1), 37–43 (1965).
  • [19] I.T. Grudinskaya and I.S. Shpak, “Effect of forest and forest strips on the moisture conditions of soils and ground water levels in the forest-steppe and steppe districts of the Ukraine”, Symposium of Hannoversch-M¨unden 1, 252–270 (1959).
  • [20] L.F. Athy, “Density, porosity, and compaction of sedimentary rocks”, AAPG Bulletin – American Association of Petroleum Geologists 14 (1), 1–24 (1930).
  • [21] Blood flow: en.wikipedia.org/wiki/Blood flow, 2009.
  • [22] M.J. Allwood and H.S. Burry, “The effect of local temperature on blood flow in the human foot”, J. Physiology 124 (2), 345—357 (1954).
  • [23] L. Landau and E. Lifszyc, Mechanics of Continuous Media, PWN, Warszawa, 1958.
  • [24] L.D. Landau and E.M. Lifshitz, Fluid Mechanics, Pergamon Press, Oxford, 1963.
  • [25] R. Wojnar, “Subdiffusion with external time modulation”, Acta Physica Polonica A 114 (3), 607–611 (2008).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPG8-0020-0017
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