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Published online by Cambridge University Press: 24 October 2008
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.
* 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.
