Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-19T00:44:49.029Z Has data issue: false hasContentIssue false
  • English
  • Français

A study of the motion of a cavity in a rotating liquid

Published online by Cambridge University Press:  28 March 2006

T. Brooke Benjamin  and
B. J. S. Barnard
T. Brooke Benjamin
Affiliation:
Department of Engineering, University of Cambridge
B. J. S. Barnard
Affiliation:
Department of Engineering, University of Cambridge Present address: Hydrodynamics Laboratory, California Institute of Technology, Pasadena.
Get access Rights & Permissions [Opens in a new window]

Abstract

Experiments are described in which a spinning tube was initially filled with water and closed at both ends; when the water had acquired uniform angular velocity the tube was suddenly opened at one end and hence emptied by centrifugal action, so that a cavity progressed along it towards the far end. The velocity of the cavity was found to be steady and proportional to the speed of rotation over the range tested, which confirmed the supposition that gravity and viscosity had insignificant effects on the cavity motion. Contrary to expectation, since the cavity velocity seemed to be too large for it to occur, the ‘Taylor phenomenon’ was observed in the liquid ahead of the cavity; that is, the motion generated by the invasion of the cavity extended over a continually lengthening region beyond it.

The theoretical discussion in § 4 explains several features of the experiments satisfactorily, although the complete analytical problem has so far proved insoluble.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 19 , Issue 2 , June 1964 , pp. 193 - 209
Copyright
© 1964 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

Benjamin, T. Brooke 1962 Theory of the vortex breakdown phenomenon. J. Fluid Mech. 14, 593.Google Scholar
Benjamin, T. Brooke & Lighthill, M. J. 1954 On cnoidal waves and bores. Proc. Roy. Soc. A, 224, 448.Google Scholar
Fraenkel, L. E. 1956 On the flow of rotating fluid past bodies in a pipe. Proc. Roy. Soc. A, 233, 506.Google Scholar
Jeffreys, H. & Jeffreys, B. S. 1946 Methods of Mathematical Physics. Cambridge University Press.
Long, R. R. 1953 Steady motion around a symmetrical obstacle moving along the axis of a rotating liquid. J. Meteorology, 10, 197.Google Scholar
Prandtl, L. & Tietjens, O. G. 1957 Applied Hydro- and Aeromechanics. New York: Dover.
Squire, H. B. 1956 Rotating Fluids, article in Surveys in Mechanics (Ed. Batchelor & Davies). Cambridge University Press.
Stewartson, K. 1952 On the slow motion of a sphere along the axis of a rotating fluid. Proc. Camb. Phil. Soc. 48, 168.Google Scholar
Stewartson, K. 1958 On the motion of a sphere along the axis of a rotating fluid. Quart. J. Mech. Appl. Math. 11, 39.Google Scholar
Taylor, G. I. 1922 The motion of a sphere in a rotating liquid. Proc. Roy. Soc. A, 102, 180.Google Scholar
Wortmann, F. X. 1953 Eine methode zur Beobachtung und Messung von Wasserströmungen mit Tellur. Z. angew. Physik, 5, 201.Google Scholar