On the Analytical Determination of the Best Form of Flows Past Bodies in a Viscous Continuum

With the help of the Prandtl equation and using the methods of the variational calculus, we have obtained equations that make it possible to analytically determine the type of contour for which the drag force in a viscous flow past a body becomes the smallest. It is rigorously proved analytically that the longitudinal cross section of a cut of well-streamlined bodies can have different forms depending on the Reynolds number. The equations found are analyzed numerically and illustrated graphically.