This problem somewhat explains the workings of some toilet valves. Open the tank

Question

This problem somewhat explains the workings of some toilet valves. Open the tank of a toilet and look at the rubber piece at the bottom that sits on the bottom but then floats after initially lifted by the turning of the flush lever. The puzzle this problem solves is this: Why does the valve stick to the bottom, but then float when lifted. a) A hollow cylinder with an open bottom (like an upside down but open can) is filled with air but is under water. What force is required to hold it under water (in terms of p, r,h,t and g? * b) The same can is on the bottom of a tank of water and its edges are sealed. The bottom is open to atmospheric air. How much force is needed to hold the can down now (so there is no force from the bottom of the tank onto the edges of the cylinder)? *

Explanation / Answer

a) Force to hold in water = Fbuoyancy   - Fweight

                                      = rhowater * pi * r^2 *l * g - rhoair * pi * r^2 *l * g

                                      = (rhowater - rhoair )* pi * r^2 *l * g

b) Force to hold at the bottom   = Po * pi *r^2              (where Po is the atmospheric pressure)

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