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The Gliding of a Plate on a Stream of Finite Depth. Part II

Published online by Cambridge University Press:  24 October 2008

A. E. Green
A. E. Green
Affiliation:
Jesus College
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Extract

7. We have discussed the gliding of a plate of finite length on a stream of finite depth. Numerical calculations have been made for the case when the angle of incidence of the plate to the stream was 30°, the results for any other angle being similar.

It was found that, for a given depth of stream and a given height of the trailing edge above the bed of the stream, the value of the lift increases with the length of the plate, until finally, when the plate is infinitely long, the lift assumes a maximum value. Further, for a given depth of stream, the total normal lift on the plate is independent of its height above the bed of the stream, when the length of the plate is small, except when the trailing edge of the plate is above the surface of the stream. Finally, when the depth of the stream is very large and the plate is near the middle of the stream, then our solution approximates to the classical Rayleigh flow past a plate in an infinite fluid.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 32 , Issue 1 , January 1936 , pp. 67 - 85
Copyright
Copyright © Cambridge Philosophical Society 1936

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References

* Green, A. E., Proc. Camb. Phil. Soc. 31 (1935), 589.CrossRefGoogle Scholar

* Tannery, J. et Molk, J., Éléments de la théorie des fonctions elliptiques, 4 (1902), 145.Google Scholar

† J. Tannery et J. Molk, loc. cit. p. 143.

* J. Tannery et J. Molk, loc. cit. p. 104.

* J. Tannery et J. Molk, loc. cit. p. 101.

* A. E. Green, loc. cit.