A few months ago I accidentally spotted an amusing phenomenon during my son’s bathtime. He has some plastic cups that he likes playing with in the bath, and as the water was running out, I took one of them, turned it upside-down, and pushed it down so that it was full of air and just above the plughole, surrounding it. If you want the hard version of the problem it is to work out what happened next. The easier version of the problem is to read past the fold, where I will say what happened, and then to explain it. I am hopeless at this kind of problem, so I don’t know the answer myself, and I also don’t rule out that the answer is too easy to be interesting. If that is the case, then apologies in advance.
What happened is (i) that the cup stayed down rather than being pushed up as it would have been if it had been above some other part of the base of the bath, and (ii) that there wasn’t a perfect seal between the rim of the cup and the surround of the plughole, so some water got in, and (iii) that water was thrown up in a kind of fountain inside the inverted cup (which I could see because the cup was slightly transparent), that lasted until almost all the water had run out.
Part of a satisfactory explanation would include an answer to the following basic question: was what I saw (and have seen several times since) a fluke that depended on the precise shape and degree of airtightness of the cup and its join to the bath, or would pretty well any plastic cup have done the job? If what one observes depends on the cup, then what is the range of possible behaviours?
Just in case it helps, and so that I can continue my series of photographs of drinking vessels, here are pictures of the plughole with and without the cup over it, but without the bathwater.