Imagine I have a clean toilet with some amount of water in the bowl. When I flush the toilet much of that water will be displaced by the tank's water. I want to work out (or model really) what amount of the original toilet bowl water will remain after the flush.
If there was B liters of water in the bowl and T liters was released from the tank I'd expect the proportion to be at most B/(B+T) of original water to tank water.. but this doesn't take into account how the water is released.
I assume this is studied in the design of toilets, so links to existing research would be interesting too! I also appreciate that it will vary for each toilet design, so feel free to answer the question for any common type or model; I'm most interested in a way of estimating or modelling it.