Yes, correspondents are correct. My remarks were pretty stupid, as they usually are. Apologies. No one needs to be told what they don’t know. I was trying to make the point that in bathtub vortex flow there is huge body of theoretical and experimental research and probably no unk-unks, in the sense that there are no unknowns. We just can’t put ‘em all together. To be constructive, the issue can be idealized to a container with an exit orifice dispensing fluid in air. Jes holdin’ up a funnel in the breeze, M’am! If the losses are small the exit flow speed at the edge of the emitted jet is approximated by V*2 =2gh, independent of the fluid density, as was hypothesized by Leonardo (c. 1500), and well known to Galileo (c.1600), Newton (c.1700) and Bernoulli (1750). If swirl vanes are introduced, then the rate of outflow is reduced, since the vortical exit flow is inclined to the vertical. If you have a narrow, long, constricted nozzle, or filters, then, a’course, again outflow is reduced, and can be calculated if these impedances are defined . If it swirls of its own accord, then, unless tests show this to be equally distributed clockwise and anti, one must assume that one’s water or funnel is twisted or God is a casuistic Jester – both quite likely. Or that the earth is spinning, a modern hypothesis, denied by the Bible, but supported by my astronaut friends who claim to have actually observed same. As Nick notes, gedanken experimenten are a wonderful source of insight and “paradoxies”, and simple kitchen experiments for this case very productive. A’course, with real experiments, a lotta control issues go without saying, so I won’t. Peter Lissaman, Da Vinci Ventures Expertise is not knowing everything, but knowing what to look for. 1454 Miracerros Loop South, Santa Fe, New Mexico 87505,USA tel:(505)983-7728 ----- Original Message -----
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