Chapter 14.10, Problem 15P

In Problem 14, the streamlines were the images of $v=$ const. Consider the flow (over the whole plane, that is, with no boundaries) with streamlines $u=$ const. This flow may be described as two vortices rotating in opposite directions. Sketch a number of streamlines indicating the direction of the velocity with arrows. since a boundary is a streamline, a flow is not disturbed by inserting a boundary along a streamline. Insert two circular boundaries corresponding to $u=a$ and $u=-a$ Show that the velocity through the narrow neck (say at $z=0$ ) is greater than the velocity elsewhere (say at $z=i$ ). You can simplify your calculation of the velocity by showing that the result in Problem 8 holds here also.