Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-18T14:56:11.026Z Has data issue: false hasContentIssue false
  • English
  • Français

Slow steady rotation of axially symmetric bodies in a viscous fluid

Published online by Cambridge University Press:  28 March 2006

R. P. Kanwal
R. P. Kanwal
Affiliation:
Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania
Get access Rights & Permissions [Opens in a new window]

Abstract

The Stokes flow problem is considered here for the case in which an axially symmetric body is uniformly rotating about its axis of symmetry. Analytic solutions are presented for the heretofore unsolved cases of a spindle, a torus, a lens, and various special configurations of a lens. Formulas are derived for the angular velocity of the flow field and for the couple experienced by the body in each case.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 10 , Issue 1 , February 1961 , pp. 17 - 24
Copyright
© 1961 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Hyman, M. A. 1954 Concerning analytic solutions of the generalized potential equation. Proc. K. Akad. Wet., Amst. A, 57, 408–13.Google Scholar
Hobson, E. W. 1931 The Theory of Spherical and Ellipsoidal Harmonics. Cambridge University Press.
Jeffery, G. B. 1915 Steady rotation of a solid of revolution in a viscous fluid. Proc. Lond. Math. Soc., 14, 327–38.Google Scholar
Kanwal, R. P. 1955 Rotary and longitudinal oscillations of axisymmetric bodies in a viscous fluid. Quart. J. Mech. Appl. Math., 8, 146–63.Google Scholar
Lamb, H. 1954 Hydrodynamics. Dover Publications.
Payne, L. E. 1952 On axially symmetric flow and the method of generalized electrostatics. Quart. Appl. Math., 10, 197–204.Google Scholar
Payne, L. E. 1956 New Isoperimetric inequalities for eigenvalues and other physical quantities. Comm. Pure Appl. Math., 9, 531–42.Google Scholar
Payne, L. E. & Pell, W. H. 1960 The Stokes flow problem for a class of axially symmetric bodies. J. Fluid Mech. 7, 529–49.Google Scholar
Schiffer, M. & Szegö, G. 1949 Virtual mass and polarization. Trans. Amer. Math. Soc. (1), 67, 130–205.Google Scholar