A note on the axisymmetric Stokes flow of viscous fluid past a spherical cap

Extract

Recent papers [1, 2, 3[ have considered dual series equations in Legendre and associated Legendre functions and have given applications of these series to various potential and diffraction problems. This note gives a further application to the problem of the axisymmetric Stokes flow of a viscous fluid past a spherical cap. The stream-function of the flow is found by solving two pairs of dual series equations in associated Legendre functions, these equations being of a form considered previously [1, henceforth referred to as DSE]. As an example a uniform flow past the cap is considered and the drag of the cap calculated. This flow has previously been investigated by Payne and Pell [4], who by a suitable limiting process derive the stream-function for the flow past the cap from the stream-function for the flow past a lens-shaped body. Their method, however, involves the use of peripolar coordinates, besides much complicated algebra, and results are given only for a cap whose semi-angle is π/2. Further, their value for the drag of this cap is incorrect.