The forces on a cylinder in a stream of viscous fluid

Abstract It has long been known that an infinite cylinder moving transversely with uniform velocity in a perfect liquid, or at rest in a uniform stream of such fluid, experiences no resistance if there be no circulation round the cylinder. The corresponding theorem in the case where circulation exists is due to W. M. Kutta and N. Joukowski, and is generally known as the Kutta-Joukowski theorem. If the velocity of the cylinder is U, there is a force transverse to the direction of motion, of amount ρUI, where I is the circulation round the cylinder and ρ the density of the fluid. This result forms the basis of the modern theory of aeroplane lift, developed in the first instance by Lanchesteri and later by Prandtl. In this theory, however, it is assumed that, at a comparatively small distance from the surface of the cylinder, the motion is strictly irrotational, and is, therefore, given by the equations which hold in a perfect fluid, the vortex motion, which involves viscosity, being limited to a “boundary layer” in the immediate neighbourhood of the cylinder and to a “wake” of which the effect is neglected after it leaves the immediate vicinity of the body.