https://www.youtube.com/watch?v=Khf6koh3IO8
Can anyone help me explain this? It seems like the ball should shoot out from underneath. I have two main theories.
1) Bernoulli's Principle says that the pressure near the waterfall is lower than the pressure on the other side, so the ball gets sucked in.
2) Magnus Effect says that the ball causes the water to change momentum as the fluid curves around the ball (i.e. the ball puts a force on the fluid, F=dP/dT). That force is responded to by an equal and opposite for the the fluid puts on the ball. Since the fluid has its momentum switched away from the waterfall, the ball has its momentum shifted TOWARDS the waterfall.
How close am I? What am I missing?
Any help would be much appreciated.
Best Answer
There are two forces that draw the ball into the waterfall (or push the ball upstream), and both of these are much stronger than the two effects mentioned in the question. As a white water kayaker, I have a lot of experience with the relevant forces, and they can both be very strong and sometimes life threatening.
The first force: in broad and uniform flows like this, there is usually an upstream circulation for a significant distance downstream of the drop. To kayakers, this flow pattern is often called "hole", "hydraulic", or "stopper". A cross section looks something like this (my own quick sketch, but there are many better illustrations by searching "whitewater" and the above terms):
As to the forces, even very small drops, like 1 ft, can create extremely powerful upstream flows. I once had a boat stay stuck in such a hole for many hours while defeating every effort to fish it out. These are surprisingly dangerous, partly because they look so innocuous, and it's easy to find discussions of this, (eg, search "low head damn rescue and fatalities"). Or, for a very tense rescue on a bigger drop, see this.
Whether the hydraulic extends to the radius of the ball is difficult to tell from the video.
The other force pushing the ball towards the waterfall is the rotation of the ball which drives it upstream. The falling water will always move faster that the bottom water, and this drives the ball to spin. This spin then pushes the ball upstream against the slower flowing bottom water. That is, in the video the drop is to the left, the ball is to right, and the spin is CCW. The fast CCW spin causes the bottom surface of the ball to be moving faster than the bottom flowing water, and which pushes the ball to the left.