The two-dimensional problem of the form of a free surface of an ideal incompressible fluid during steady flow from a rectangular channel through a thin slot with simultaneous uniform delivery of fluid through the side walls is examined. Forces of gravity and surface tension are taken into account. The nonlinear problem of the simultaneous determination of the free surface and velocity field of the fluid is solved by the iteration method. Convergence of the iterations to the solution of the problem for small values of the parameters is investigated. The solution of the linearized problem is obtained in a closed form for a small depth of the discharge and small width of the channel, which is compared with the solution of the problem in a complete formulation. Graphs of the free surface of the fluid for different values of the parameters, obtained as a result of numerical solution of the nonlinear problem, are presented.
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L. D. Landau and E. M. Lifshits, Mechanics of Continuous Media [in Russian], Gostekhizdat, Moscow (1954).
N. N. Moiseev and V. V. Rumyantsev, Dynamics of a Body with Cavities Containing Fluid [in Russian], Nauka, Moscow (1965).
S. N. Antontsev, O. F. Vasil'ev, B. G. Kuznetsov, and N. N. Yanenko, “Numerical calculation of a spillway,” in: Certain Problems of Computational and Applied Mathematics [in Russian], Nauka, Novosibirsk (1966).
V. S. Temkina, “Two-dimensional problem of the flow of fluid from an infinite layer,” in: Problems of Hydrodynamics and Heat Transfer in Cryogenic Systems [in Russian], No. 4, Khar'kov (1974).
L. A. Temkhin, V. S. Temkina, and G. V. Shcherbina, “Numerical solution of certain problems of the dynamics of fluid with a free surface,” in: Transactions of the Republic Conference “Computational Mathematics in Modern Scientific—Technical Progress” [in Russian], Kanev (1974), pp. 346–354.
V. S. Temkina, “First approximation in the problem of steady flow of a fluid with consideration of surface forces,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 6 (1974).
G. V. Shcherbina, “Form of the free surface of an ideal incompressible fluid,” in: Collection of Scientific Works of the Physicotechnical Institute of Low Temperatures [in Russian], Izd. Akad. Nauk UkrSSR, No. 1 (1969).
V. B. Erenburg, “Two-dimensional stationary problem with a free boundary and boundary angle for the Euler equation,” in: Fluid Dynamics [in Russian], No. 14, Novosibirsk (1973).
N. M. Krylov and N. N. Bogolyubov, “Approximation solution of the Dirichlet problem,” Dokl. Akad. Nauk SSSR, Ser. A, No. 12 (1929).
Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 67–75, January–February, 1977.
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Temkina, V.S. Form of a free surface during steady flow of a capillary fluid in a rectangular channel. Fluid Dyn 12, 55–63 (1977). https://doi.org/10.1007/BF01074625
- Surface Tension
- Free Surface
- Velocity Field
- Closed Form
- Side Wall