Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-24T16:24:29.710Z Has data issue: false hasContentIssue false
  • English
  • Français

Rayleigh's problem for a semi-infinite plate

Published online by Cambridge University Press:  24 October 2008

L. Howarth
Get access Rights & Permissions [Opens in a new window]

Extract

The problem considered in this paper is the fluid motion arising from a thin semi-infinite plate started to move impulsively from rest (in viscous incompressible fluid at rest) with a velocity, subsequently maintained uniform, parallel to the edge. Two solutions are given, one obtained in polar coordinates is in the form of an infinite series, whilst the other, derived operationally in parabolic coordinates, leads to a single integral for the velocity distribution. The former is convenient for computation in the vicinity of the edge, the latter being more convenient elsewhere.

A hypothesis originally introduced by Rayleigh after he had discussed the corresponding flow for an infinite plane has been used here to draw deductions about the steady flow past a quarter-plane whose leading edge is normal to the direction of flow and also to obtain approximate expressions for the effect of the edges on the skin friction of a sufficiently broad rectangle whose length is parallel to the incident stream.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 46 , Issue 1 , January 1950 , pp. 127 - 140
Copyright
Copyright © Cambridge Philosophical Society 1950

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)Rayleigh, Lord.Phil. Mag. (6), 21 (1911), 697–711; Scientific Papers, 6, 39, 40.CrossRefGoogle Scholar
(2)Gunn, J. C.Philos. Trans. A, 240 (1947), 327–73.Google Scholar
(3)Lamb, H.Proc. London Math. Soc. (2), 4 (1906), 190.Google Scholar
(4)Sommerfeld, A.Math. Ann. 17 (1895), 317.Google Scholar
(5)Carslaw, H. S.Mathematical theory of the condition of heat in solids, 2nd ed. (London, 1921).Google Scholar
(6)Watson, G. N.Treatise on the theory of Bessel functions, 2nd ed. (Cambridge, 1944).Google Scholar
(7)Carslaw, H. S. and Jaeger, J. C.Operational methods in applied mathematics, 1st ed. (Oxford, 1941).Google Scholar