The lift and moment on a flat plate in a stream of finite width

Abstract

1. The problem of the lift on a flat plate in a stream between parallel rigid walls has been solved in an exact form, by using a suitable conformal transformation, by Tomotika (1934), who also gives an expansion for the lift in the particular case when the mid-point of the plate is midway between the walls; a similar solution for the moment on the plate does not seem to have been given. The method used in the following paper is quite different and is, perhaps, of sufficient interest to justify further examination of the problem. The flat plate is treated as the limiting case of an elliptic cylinder, and the method of solution leads directly to expansions for the lift and for the moment suitable for any position of the plate subject to the parameters being within the range necessary for convergence. Moreover, by a simple modification, expansions for lift and moment are obtained when the stream is bounded by parallel free surfaces, taking the boundary condition in an approximate form; and a further modification gives the corresponding results when one surface is rigid and the other free. A brief examination is also made of the moment for an elliptic cylinder.