XXXI. The flow of viscous fluids round plane obstacles

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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 8πμCU, μ, 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 w-all is shown to be 2S2/3πμs 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.

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