Application of the Displacement Hypothesis to Find the Resistance to a Viscous Fluid Flow Around Bodies

Abstract

The hypothesis of fluid displacement by a flow around body is investigated, which consists in the fact that the resistance force to a slow flow of a viscous fluid around a body is proportional to the volume of fluid displaced by the body, both due to the replacement of the fluid by the body itself and due to the hydrodynamics of the boundary layer near the body. This hypothesis is confirmed by the example of the flow around a ball and an infinitely thin flat plate. On the basis of this hypothesis, the force of resistance to the across flow around the cylinder and the longitudinal flow around the ellipsoid of rotation are found.