In reply to Horace Heffner's message of Thu, 31 Mar 2005 13:43:54 -0900: Hi Horace, [snip] >>I'm having some trouble understanding this formula. If it's meant >>to give the relationship between the absolute height of the water >>surface at any radius, then it seems to say that at w=0, h= h0, >>i.e. h0 is the height of stationary water in the tank. > >The variable h0 is merely a constant that allows positioning the parabolic >surface cross section at the right elevation. > >> >>>Correction follows. Sorry! >>> >>>The shape of the final equilibrium surface is: >>> >>> h = (w^2/2g) x R^2 + h0 >> >>However when the water rotates, a dip forms at the middle, which >>can drop right down to the floor of the tank at sufficiently high >>w. However, according to the formula, for any w > 0, h > h0 for >>all R, since the first term is always positive. > >The h0 above is negative. > If h = (w^2/2g) x R^2 + h0 and h0 is negative, then for w=0, h=h0 and is thus also negative. How does one end up with a negative height?
Or should the original formula perhaps be: h = h0 - (w^2/2g) x R^2 ? (Since the second term in this version is positive, the height becomes less for higher w and also for smaller R, both of which make sense). In short, is h the distance up from the bottom of the tank, or the distance down from the surface? Regards, Robin van Spaandonk All SPAM goes in the trash unread.
