Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-24T16:15:40.061Z Has data issue: false hasContentIssue false
  • English
  • Français

Slow motion of viscous liquid in a semi-infinite channel

Published online by Cambridge University Press:  24 October 2008

W. R. Dean
W. R. Dean
Affiliation:
Trinity CollegeCambridge
Get access Rights & Permissions [Opens in a new window]

Extract

1. A slow two-dimensional steady motion of liquid caused by a pressure gradient in a semi-infinite channel is considered. The medium is bounded by two parallel semi-infinite planes represented in Fig. 1 by the straight lines AB, DE. The stream-function ψ is a biharmonic function of x, y which exactly satisfies the condition that AB, DE must be stream-lines, but the condition that there must be no velocity of slip on these boundaries is satisfied only approximately, and the calculated velocity of slip gives a measure of the accuracy of the solution.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 47 , Issue 1 , January 1951 , pp. 127 - 141
Copyright
Copyright © Cambridge Philosophical Society 1951

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

REFERENCES

(1)Stanton, T. E., Marshall, D. and Bryant, C. N.Proc. Roy. Soc. A, 97 (1920), 413–34.Google Scholar
(2)Taylor, G. I.Proc. Roy. Soc. A, 166 (1938), 476–81.Google Scholar
(3)Dean, W. R.Proc. Cambridge Phil. Soc. 32 (1936), 598–613.CrossRefGoogle Scholar
(4)Rosenhead, L.Proc. Roy. Soc. A, 175 (1940), 436–67.Google Scholar