The ghastly thing happened again to me. I was taking a bath (this is NOT the ghastly thing; one has to deal with it now and then, pretty much like the intermediate boss levels in games), and I simply couldn’t get the hot-cold balance and the amount right. I could get reasonably close to the desired in about 10 minutes; but there was still a slight drift towards (alternatingly)hot/cold over time; not very pleasing. Result: By the time I am satisfied with the settings, I decided that I was done for now.
Now, by a coincidence, I am taking a Control Systems course this semester, so naturally, I started applying all sorts of mathematical models and stuff. So, my turning of the taps would be input; the final water temperature AND speed would be the output. The “system” would comprise of some complicated heat transfer and fluid mechanics. One solid fact I have realized:
Have pity on Hot water taps; they’ll will be a lot happier in time domain than the s-domain.
In general, going over to some imaginary world where every single object around us has been put through a Laplace Transform (I am not sure what I mean, but Elec has taught me that it doesnt matter as long as I have the math to back it up).
Besides that one, I could make many interesting observations while adjusting the taps. One myth buster: when you switch on the cold tap full blast in the middle of things, it doesn’t suddenly force out the pipe’s contents and come gushing out as a hundred percent cold blast; it instead smoothly merges over and asymptotically becomes cold. I am already thinking first order systems.. this is what the Controls course does to you, I guess, but I dare not stand the sight of those Transforms again.
P.S. On a happy note, I have actually consumed a decent amount of soap this semester; this one lasted me 3 semesters. My mom will be happy to see me buy a new one.