Advertisement

Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Flow of a viscous fluid around a sphere of finite radius

Abstract

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.

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

References

  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.

Download references

Author information

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Ovseenko, Y.G. Flow of a viscous fluid around a sphere of finite radius. J Appl Mech Tech Phys 9, 202–204 (1968). https://doi.org/10.1007/BF00913185

Download citation

Keywords

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