Here's the question you clicked on:
flumech2
Are velocity components Vr=5rcos(theta), Vtheta = -5rsin(theta) irrotational?
|dw:1362718452343:dw| I don't know if it helps you, but it's what I figured out by looking at it.
If you convert to rectangular coordinates, \(\large v_x=5r=5\sqrt{x^2+y^2}\) \(\large v_y=0\) Then \(\large \partial v_x/\partial y \neq \partial v_y/\partial x \) so this velocity is not irrotational.