Quite a few years ago, I had an argument with my mother (who was supported in this and other arguments by my young wife, of all people). My mother asserted that taking showers used less water than taking a bath. Horrified I argued that how much shower water was used would depend on how long you stood in the downpour.
That position led to my suffering inexplicable family derision for the next 41 years, but today I had a moment worthy of Archimedes, whose principle is fundamental to fluid mechanics. I decided to time how long it took to fill the bath. That would tell me how long I could stand in the shower while using exactly one tubful of water.
The answer was less than five minutes.
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