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Form of a free surface during steady flow of a capillary fluid in a rectangular channel

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Abstract

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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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

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Keywords

  • Surface Tension
  • Free Surface
  • Velocity Field
  • Closed Form
  • Side Wall