Article,
The flow of viscous fluids round plane obstacles
The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Series 7, 40 (302): 338-351 (1949)
DOI: 10.1080/14786444908561255
Abstract
In certain cases of slow viscous flow round thin plates the solution of Stokes equations can be reduced to a solution of Laplace's equation with simple boundary conditions, the flow being thus relatable to the potential distribution in an electrostatic position. It is shown that the force on a plate held perpendicular to a stream of velocity U is 8π?CU, ?, being the viscosity of the fluid and C the electrical capacity of a conductor of the same shape as the plate. The rate of flow of fluid through an elliptic aperture in a thin wall is shown to be 2S^2/3πμs times the pressure difference between the two sides, S being the area of the aperture and s its perimeter. A simple expression is also derived for the torque on an elliptic plate rotating about its minor axis. Approximate methods for dealing with the flow past plates of complicated shapes are described, and the case of a paddle-type viscometer is treated as an example.
