Physics — On Oseen’s theory for the approximate determination of the flow of a fluid with very small friction along a body

Abstract

The determination of the flow of a viscous fluid along a body of given contour is one of the most important problems of hydrodynamics. When we consider the stationary flow along a body at rest and start from the equations of motion for an incompressible viscous fluid, the solution is required of a system of four partial differential equations with the velocity components and the pressure as variables. This solution has to satisfy the boundary conditions, which for the case are that the velocity of the fluid along the surface of the body is zero, and that at infinity the flow asymptotically approaches to a parallel motion with given constant velocity. In the following we will suppose that this latter velocity has the value V and is directed along the negative x-axis. Until now the rigorous solution of these equations presents unsurpassable difficulties. However, many applications of hydrodynamics do not require a solution of general validity, but a solution for the case in which the internal friction of the fluid is very small and may be put nearly equal to zero. We shall confine ourselves to this case.