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The moment of the fluid forces acting on a plate which is gliding on the surface of a stream

Published online by Cambridge University Press:  24 October 2008

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

13. Formulae have been obtained for the moment of the fluid forces which act on a plane plate which is gliding on the surface of a stream of finite or infinite depth. It has been shown that the formulae for the lift and moment forces acting on a plate which is gliding on a stream of infinite depth may be obtained by a limiting process from the formulae for the general case of gliding on a stream of finite depth. Also, by another limiting process, the lift and moment forces for the Rayleigh flow past a flat plate in an infinite stream have been obtained from the lift and moment forces for gliding on a stream of infinite depth.

Numerical work has been carried out for the case when the angle of incidence of the plate to the stream is 5° and this has shown the variation of the lift and moment forces and the position of the centre of pressure with a range of values of the length of the plate, the depth of the stream and the height of the trailing edge of the plate above the bed of the stream.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 34 , Issue 2 , April 1938 , pp. 167 - 184
Copyright
Copyright © Cambridge Philosophical Society 1938

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References

* Green, A. E., Proc. Cambridge Phil. Soc. 31 (1935), 589,CrossRefGoogle Scholar denoted here as paper A; Proc. Cambridge Phil. Soc. 32 (1936), 67,Google Scholardenoted here as paper B; Proc. Cambridge Phil. Soc. 32 (1936), 248,Google Scholardenoted here as paper C.

† This has been done already for the lifting force, in paper C p. 251.

* See paper B, pp. 72, 73. In equation (27) of this paper read K/σ(ω1) for K, and in equation (31) read A/σ2(ν) for A.

* Paper B, pp. 77, 78.

* The series for z may be differentiated, since we originally obtained z by integrating a series for dz.

* See Lamb, , Hydrodynamics, 6th ed. (Cambridge, 1932),Google Scholar § 77.

† Not c, as stated in paper C.

‡ Wagner has shown that the expressions for the lifting forces agree in these two cases.

* In order to get these curves into as small a space as possible without overlapping it was necessary to use many different scales for plotting. The curves are marked with the letters a to f and the corresponding ordinates are given below the figures.