What is Proof of circle theorem in fluid?

Answer 1

Since z = a^2/z on the circle, we see that w as given by (1) is purely

real on the circle C and therefore if* = 0. Thus C is a streamline.

If the point z is outside 0, the point az

/z is inside 0, and vice-versa. Since

all the singularities off(z) are by hypothesis exterior to C, all the singularities

off(a?/z) are interior to C ; in particular f(a

z

/z) has no singularity at infinity,

since f(z) has none at z = 0. Thus w has exactly the same singularities as/(z)

and so all the conditions are satisfied.