The forces on a solid body in a stream of viscous fluid

The object of the present investigation is to obtain formulae for the lift and drag when a solid body of any shape is at rest in a stream of incompressible viscous fluid, but no limitation is imposed upon the magnitude of the stream velocity. It is convenient to start by giving a short account of previous work along the same lines. The forces on a cylinder of any shape in a stream of viscous fluid have been discussed by FILON.* Writing U for the velocity of the stream, andu ,v ,w for the additional disturbance velocities, and neglecting terms of second order in the disturbance, FILON obtains a system of linear equations identical with those adopted by OSEEN. These equations, however, are only assumed to be valid at a great distance from the cylinder, and not at the surface of the solid, as in the applications made by OSEEN and other writers. The complete solution of the equations is obtained in the form of two series of typical solutions, in which the corresponding motion is respectively rotational and irrotational. The lift on the cylinder is found to be given by the same expression as in the KUTTA-JOUKOWSKI theorem for a perfect fluid. Also the drag is found to be associated with a particular term in the solution, which corresponds to an inward flow along the tail and a compensating outward flow across a large contour.