Splash Physics: A Practical Application When you're peeing into a toilet containing clean water, and some of the water splashes back at you, is it more likely clean water is splashing onto you or pee?
 A: A somewhat gross question, but nevertheless interesting if you consider a stream of fluid in general entering a still basin with the same fluid. The question of what's thrown back, or even are there conditions where you don't get anything thrown back.
I don't believe there are any first principle physics, theories or equations that could predict the outcome of whether the water in the basin, the water in the stream or a combination of the two is what's thrown back from the basin. It's probably very sensitive to angles, velocity when it hits the water, and depth of the basin.
Try experiments with a bowl of clear water and a separate container with a nozzle or spout in the bottom and containing water with dye. My guess is you will get both fluids thrown from the container in most any situation.
And with regards to 'clean' water in the toilet bowl. I don't believe that exists even after several flushes.
A: An impact in liquid in a bowl (or even in the center of a water goblet)
creates a ring wave that propogates outward, reflects from the bowl rim, then propogates back toward the center.  When that wave focuses at a point, it can throw up a spout and eject some droplets.
Urine flow turns into separate drops before it hits the porcelain pot, and each such
drop can cause a wave that, on reflection, ejects droplets.  The ejecta, however, does NOT come from the input, but from the surface of the bowl's liquid content, and is ejected at a time delay from the input event.   So,
it's diluted, mainly water.
