Assume a flow enters the vertical pipe's inlet at a uniform speed $v=v_0$ (so zero vorticity) and flows out of the pipe under gravity.
My question is will the three particles $A, B$, and $C$ cross the "Finish line" at the same time?
I think they should because otherwise, it feels like some vorticity has been introduced by gravity, which shouldn't happen.
But if they do, then the blue streamline has a slower speed, since it travels the shortest path. But doesn't this mean there is vorticity present at the point $P$ (or somewhere near the bend)?
