Discontinuous fluid motion past a curved boundary

AIthough many writers have devoted their attention to the problem of the motion of a fluid past a curved boundary, no method so simple, yet so effective, as that developed for the case of a plane barrier by Kirchhof and others, and since elaborated by Mitchell, Love, Bryan and Jones, etc., has been discovered for the more general ease. Within the past few years a group of mathematicians in Italy and in France, in particular Levi-Civita, Cisotti, and Villat, and J. G. Leathem in this country, have published notable advances on this subject. In aeronautics alone recent developments have shown the practical necessity for an effective discussion of the case where the plane is cambered. In this paper I propose to show how two-dimensional problems of the motion of a curved surface through a fluid, or the efflux of fluid through an orifice in a vessel of any shape, may be solved, how to find the form of the free stream-line, and bow the components of resistance may be calculated from the solution obtained. It will be assumed that the fluid is of vanishingIy small viscosity, that the motion is two-dimensional and steady, and that the surface in its motion gives rise to a free stream-lino, along which the pressure, and therefore the velocity, is constant, extraneous forces such as gravity being neglected.