Some exact results for plane incompressible flow

Abstract

Simple results are derived from an exact conformal transformation of the flow field about a lifting circular cylinder at an angle of attack in incompressible flow to that about a profile. The mapping function is one proposed by Moriya several decades ago which stretches the field at great distances from the foil and is here used to derive a two-parameter family of symmetrical shapes. The geometry and flow speed are easily evaluated at arbitrary points on the profile surface and hence errors can be readily defined for evaluation of numerical predictions. The strength of equivalent contour distributions of sources, vortices and dipoles is also given.