Here's something you could try, based on a passage from Richard Feynman's "Surely You're Joking, Mr. Feynman!":
When I was in high school, I'd see water running out of a faucet growing narrower, and wonder if I could figure out what determines that curve. I found it was rather easy to do. I didn't have to do it; it wasn't important for the future of science; somebody else had already done it. That didn't make any difference. I'd invent things and play with things for my own entertainment.
Assume a constant flow rate, and see whether your students can be guided to a solution. You might try a warm-up problem, where you pour water into a non-cylindrical glass (a martini glass, or something more weirdly shaped) and try to determine how quickly the level rises, as a function of cross-sectional area.
