Hostname: page-component-848d4c4894-sjtt6 Total loading time: 0 Render date: 2024-07-03T14:33:14.606Z Has data issue: false hasContentIssue false
  • English
  • Français

The motion of a cavity in a vertical rotating tube

Published online by Cambridge University Press:  29 March 2006

R. Collins  and
M. T. Hoath
R. Collins
Affiliation:
Department of Mechanical Engineering, University College London
M. T. Hoath
Affiliation:
Department of Mechanical Engineering, University College London
Get access Rights & Permissions [Opens in a new window]

Abstract

Experiments are performed to measure the upward velocity U of the cavity resulting from the draining of a vertical liquid-filled tube of radius b, which rotates about its axis at various speeds. With no rotation the cavity moves so that the Froude number U/(gb)½ is constant, where g is the gravitational acceleration. For high angular velocities Ω, however, the cavity appears to adopt a constant value of the Rossby number U/Ωb, implying that gravitational forces are dominaked by centrifugal forces. The cavity velocity finally achieved is found to be the same as the maximum group velocity of infinitesimal waves, so that U/Ωb = 0.52. Approximate theoretical models which satisfactorily describe the development of the motion are constructed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 57 , Issue 3 , 20 February 1973 , pp. 515 - 527
Copyright
© 1973 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

Batchelor, G. K. 1967 Am Introduction to Fluid Dynamics, p. 546 & p. 476. Cambridge University Press.
Benjamin, T. B. 1968 J. Pluid Mech. 31, 209.
Benjamin, T. B. & Barnard, B. J. S. 1964 J. Fluid Mech. 19, 193.
Collins, R. 1965 J. Fluid Mech. 22, 763.
Davies, R. M. & Taylor, G. I. 1950 Proc. Roy. SOC. A 200, 315.Google Scholar
Dumitrescu, D. T. 1943 2. angew. Math. Mech. 23, 139.
Fraenkel, L. E. 1956 Proc. Roy. SOC. A233, 506.
Garabedian, P. R. 1957 Proc. Roy. SOC. A 241, 423.
Layzer, D. 1955 Astrophys. J. 122, 1.
Squire, H. B. 1956 Surveys in Mechanics (ed. G. K. Betchelor & R. M. Davies), p. 139. Cambridge University Press.
Zukoski, E. E. 1966 J. Fluid Mech. 25, 821.