The flow pattern around a spinning cylinder

The flow pattern around the spinning cylinder is also altered as the strength of the circulation increases. In Fig. 3.25 when Г = 0 the flow pattern is that associated with the previous non-spinning case with front and rear stagnation points Si and S2

respectively, occurring on the horizontal axis. As Г is increased positively a small amount the stagnation points move down below the horizontal axis.

Since from the equation for the velocity anywhere on the surface

qi = 2U sin 6 + -— = 0 at the stagnation points
6 = arcsin(—T/AnaU)

which is negative. As Г is further increased a limiting condition occurs when 6 — —тт/2, i. e. Г = AnaU, the stagnation points merge at the bottom of the cylinder. When Г is greater than Aira U the stagnation point (S) leaves the cylinder. The cylinder continues to rotate within the closed loop of the stagnation streamline, carrying round with it a region of fluid confined within the loop.