A modification of Oseen’s approximate equation for the motion in two dimensions of a viscous incompressible fluid

Abstract This paper is concerned with the steady motion in two dimensions, past a fixed cylindrical body, of an incompressible fluid possessing finite viscosity. Alternatively, the fluid may be imagined to be stationary at infinity, and the cylinder to move through it with uniform velocity in a direction normal to its own axis. The problem has importance for aeronautics, since a solution would permit the calculation of what in modern aerofoil theory is termed the “ profile drag.” 2. Treating the cylinder as fixed, we take rectangular axes Ox, Oy, Oz, of which 0z is along its axis and Ox is the direction of the undisturbed stream (i.e., of the flow at infinity). The motion of the fluid is then defined by component velocities u, v in the directions Ox, Oy respectively.