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Flow of a viscous fluid around a sphere of finite radius


We consider the stead y flow of a viscous fluid around a sphere of finiteradius in non-linear formulation. The equations of motion are written in non-dimensional terms. We seek their solution as the expansion of the unknown stream function in a series of powers of the Reynolds number, the coefficients of which are polynomials in associated Legendre functions of the first kind. Recurrence relations are given for the sequential determination of all coefficients. The velocity and pressure fields are determined. The drag is calculated. Numerical calculations are carried out.

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  1. 1.

    F. K. G. Odqvist, “Uber die Randwertaufgaben der Hydrodynamik Zaber Flüssigkeiten,” Math. Zeitschrift., 32, no. 3, 1930.

  2. 2.

    Yu. G. Ovseenko, “Motion of a viscous fluid between two rotating spheres,” Izv. VUZ,., Matematika, no. 4, 1963.

  3. 3.

    C. W. Oseen,” Über die Stokes'sche Formel und Über eine verwandte Aufgabe in der Hydrodynamik, “, Arkiv. Matematik, Astr. og Fys., VI, 29, 1910.

  4. 4.

    I. Praudman and D. Pearson, “Expansions in small Reynolds numbers for problems of flow around a sphere and a circular cylinder,” Mekhanika, [Russian translation] 2 (48), 1958.

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Ovseenko, Y.G. Flow of a viscous fluid around a sphere of finite radius. J Appl Mech Tech Phys 9, 202–204 (1968).

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  • Mathematical Modeling
  • Reynolds Number
  • Mechanical Engineer
  • Numerical Calculation
  • Industrial Mathematic