Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-28T22:09:50.458Z Has data issue: false hasContentIssue false
  • English
  • Français

The stability of viscous flow between rotating concentric cylinders with a pressure gradient acting round the cylinders

Published online by Cambridge University Press:  28 March 2006

R. C. Diprima
R. C. Diprima
Affiliation:
Department of Mathematics, Rensselaer Polytechnic Institute, Troy, New York
Get access Rights & Permissions [Opens in a new window]

Abstract

The stability of a viscous fluid between concentric cylinders is analysed, for the case in which the basic velocity distribution is the sum of a velocity distribution due to the rotation of the cylinders (Taylor 1923), and a ‘pumping’ velocity distribution due to a pressure gradient acting round the cylinders (Dean 1928). The critical Taylor number is computed for a wide range of values of the ratio of average velocity of pumping to average velocity of rotation for the case in which the outer cylinder is stationary. It is assumed that the spacing between the cylinders is small.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 6 , Issue 3 , October 1959 , pp. 462 - 468
Copyright
© 1959 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

Brewster, D. B., Grosberg, P. & Nissan, A. H. 1959 Proc. Roy. Soc. A, 251, 76–91.
Brewster, D. B. & Nissan, A. H. 1958 Chem. Engng Sci. 7, 215–221.
Chandrasekhar, S. 1954a Amer. Math. Mon. 7, 61, 32–45.
Chandrasekhar, S. 1954b Mathematika, 1, 5–13.
Dean, W. R. 1928 Proc. Roy. Soc. A, 121, 402–420.
DiPrima, R. 1955 Quart. Appl. Math. 1, 13, 55–62.
Hämmerlin, G. 1958 Arch. Rat. Mech. Anal. 3, 1, 212–224.
Pellew, A. & Southwell, R. V. 1940 Proc. Roy. Soc. A, 176, 312–344.
Reid, W. 1958 Proc. Roy. Soc. A, 244, 186–198.
Taylor, G. I. 1923 Phil. Trans. A, 223, 289–343.