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$$\pmb { \underline { \text {Tougher Case }}}(L_{Pipe} \neq 0)$$ Since the information that there is a long pipe between the Hose and the tank was unknown therefore I would use a better model i.e., Poiseuille Flow Equation. Poiseuille Flow equation for fluid motion in pipe states that: $$\Delta p = \frac {8L \eta \pi v_{out}}{A}$$ i.e., $$v_{out} = \... 3 I noticed that if you push the potato against the bottom surface the water starts to bubble quite a lot even if the water is not that hot. Pressing the flat faces of the half-potatoes against the bottom of the pan causes the thickness of the water layer (between potato and pan bottom) to be reduced strongly. This in turns makes the thinned water layer ... 2 Water doesn’t change density significantly. Even at the bottom of the ocean, effects due to temperature and salinity are much larger than those for pressure. The c.m. will be in the center of the uniform mass: h/2. So it will rise as you add water and increase h. 2 In the case of fingers turning the pages of a book, the water or spit you put on your fingers is quickly absorbed into the paper, which pulls the paper into close contact with your skin and makes them stick together by surface tension forces. This increases the friction coupling between your fingertip and the paper, and helps lift the page you are turning ... 2 Water flows by capillarity both ways. But the flow from the glass with higher level will be greater because it needs a smaller hill to climb. When levels are equal, flow from both directions equalize. 1 The gravity scenario is not that hard to grasp, if you have the right example. I'll try to provide one here. We begin with a large container of water and drop a bowling ball into it from a large height. The ball strikes the water surface and as it descends into the water, it pushes the water in front of it sideways to get it out of the way. Now we have ... 1 When some substance is suffering a phase transition, the particles are rearranging their “configuration”. Our intuition says that when we have gas, particles are more separated from each other and when we have something solid they are really compacted. In water something different happens, when freezing water change the configuration of the particles that ... 1 As others have pointed out, water is very well approximated as an incompressible fluid. To answer your question, however, suppose you had some material which had a density which varies spatially, so \rho = \rho(\mathbf{x}). Then the center of mass \mathbf{R} is readily obtained by$$\mathbf{R}=\frac{1}{M} \int \mathbf{r} \rho(\mathbf{r}) d^3 x. For ...