Chapter 3, Problem 3.21P

Consider the streamlines over a circular cylinder as sketched at the right of Figure 3.26. Single out the first three streamlines flowing over the top of the cylinder. Designate each streamline by its stream function, ${\psi }_1,{\psi }_2$ and ${\psi }_3$. The first streamline wets the surface of the cylinder: designate ${\psi }_1=0$. The streamline above that is ${\psi }_2$ and the next one above that is ${\psi }_3$. Assume the streamlines start out in the freestream equally spaced. Hence, the volume flow rates between the streamlines are the same. The streamline ${\psi }_2$ passes through the point $\left(1.2R,\pi /2\right)$ directly above the top of the cylinder. Calculate the location of the point directly above the top of the cylinder through which the streamline ${\psi }_3$ flows. Comment on the spacing between the streamlines directly above the top.