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The ping pong balls are still a bit of a mystery then aren't they - is there any chance you could toss some kind of tracking device in there?

GPS could be helpful on a large scale if it did go underground for a distance, but I'm wondering about either setting up some kind of a local high-resolution tracking system that can track objects in the water, or some kind of a gyroscopically-aware tracking device that could be placed into the water and transmit telemetry from inside the kettle itself!

Could you model the current of the water while it's out of sight?

GPS signals also penetrate maybe a few centimeter water before they're unusable. Water is astoundingly good at blocking GPS.
In churning water with a lot of air, their movement is probably pretty chaotic. Afterwards whether they tend to float, or are weighted, they could get hung up on any place where the channel isn't smooth. There could be an enormous subterranean cavern that would hold trainfuls of ping-pong balls somewhere along the water's path, too.
Why not put some color and see if it showed up instead of ping pong balls?
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The comment was not meant for researchers but instead for those DIY people who were trying to figure out by pouring ping pong balls.