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On the steady motion of viscous liquid past a flat plate

Published online by Cambridge University Press:  26 February 2010

W. R. Dean
W. R. Dean
Affiliation:
University College, London
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Extract

A method of assessing the accuracy of an approximation to the steady two-dimensional flow of viscous incompressible liquid past a flat plate is developed. The approximate solution, with stream-function ψ1 is closely related to the boundary-layer solution, and is expressed in terms of the function used in that theory. The conditions at the surface of the plate and at infinity are exactly satisfied by ψ1 but the equation of (finite) motion is not exactly satisfied. However, ψ1 is an exact solution of a problem in fluid motion, if a body force, of appropriate magnitude depending on ψ1 is assumed to act on the fluid. The magnitude of this force provides a criterion of the accuracy of ψ1, and some use has been made [5] of this means of estimating accuracy. This criterion is, in effect, only qualitative, since it is not possible to make a numerical estimate of the effect on the motion of a body force which is non-conservative and acts over the whole field of flow.

Type
Research Article
Information
Mathematika , Volume 1 , Issue 2 , June 1954 , pp. 143 - 156
Copyright
Copyright © University College London 1954

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References

1.Dean, W. R., Proc. Cambridge Phil. Soc., 50 (1954), 125–30.CrossRefGoogle Scholar
2.Dean, W. R. and Harris, G. Z., Mathematika, 1 (1954), 18–23.CrossRefGoogle Scholar
3.Goldstein, S. (Editor), Modern Developments in Fluid Dynamics, vol. 1 (Oxford, 1938), 135.Google Scholar
4.Howarth, L., Proc. Roy. Soc. A, 164 (1938), 547–79.Google Scholar
5.Lamb, H., Hydrodynamics, 6th edn. (Cambridge, 1932), 609–14.Google Scholar
6.Love, A. E. H., Mathematical Theory of Elasticity, 4th edn. (Cambridge, 1934), 489–91.Google Scholar