In reply to Horace Heffner's message of Fri, 11 Mar 2005 07:45:11 -0900: Hi, [snip] >direction the water goes down the drain. Any angular momentum exhibited by >the vortex must be there initially, and some of that is lost by transfer to >the tank bottom. > >In all cases the overall angular momentum is conserved. [snip] Correct, but not really the issue. I had already assumed that such was the case. The issue is where does the *energy* come from?
Put simply, 1 kg of water that changes it's radius by a factor of 10, undergoes roughly[1] a ten fold velocity increase. This implies a 100 fold kinetic energy *increase*. Where does that energy come from? It can't all come from gravity, because gravity can only supply a fixed amount, equal to m x g x h, whereas the increase in energy is a function of the initial velocity, and is therefore different for each initial velocity, and consequently not always equal to m x g x h. You pointed out that angular momentum goes down the drain with the water. This is something I hadn't really considered, but it only serves to sharpen the problem. It is precisely the angular momentum that goes down the drain, which is *not* passed out of the system before the drain is reached. [1] In fact it will be slightly less, due to friction as you pointed out. Making the tank deeper will reduce this loss on average, because friction with the bottom will apply to a smaller fraction of the water. Or if you prefer, we can fill it with liquid helium instead, so that there is no friction. Regards, Robin van Spaandonk All SPAM goes in the trash unread.
