The forces on a body placed in a curved or converging stream of fluid

Abstract

The force which a body experiences when placed in a converging stream of fluid has a certain practical interest in aeronautics because the flow in the centre of a parallel-walled wind tunnel is of this type. The convergence is due to the retardation of a layer of air close to the walls. This retarded layer increases in thickness as the air passes down the channel, thus causing a corresponding increase in the velocity in the central part of the channel. This increase in velocity is associated with a decrease in pressure in accordance with Bernouilli’s equation, the pressure in a Pitot tube being very nearly constant down the channel at all points outside the retarded layer. In measuring the resistance of models of airships it has been customary to correct the observed readings by subtracting what is called the “horizontal buoyancy,” i. e. , the force which would act on the body if the air were a stationary fluid in which the existing pressure gradient down the channel was maintained by some external force like gravity. Expressed mathematically, if dp / dx is the pressure gradient, i. e. , the gradient of static pressure in the channel, and V the volume of the body, the “horizontal buoyancy” is — V dp / dx . This correction to the measured resistance of an airship model is believed to be approximately correct from the point of view of wind tunnel practice, and the primary object of the present work was to find out how far it is justified from the point of view of hydrodynamical theory.