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Derivation of the shape of a clepsydra

  1. Dec 17, 2009 #1
    1. The problem statement, all variables and given/known data
    Clepsydra was a water clock used in old times in which water was allowed to espace through a small hole at the bottom. Find the shape of the clepsydra, if the water level is to fall at a constant rate.


    2. Relevant equations
    Torricelli Law


    3. The attempt at a solution
    No clue.
     
  2. jcsd
  3. Dec 17, 2009 #2

    HallsofIvy

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    The point is that water falls at a constant rate- that is, the volume of water is reducing at a constant rate dV/dt. If you know the shape of the curve forming the walls (I would assume a volume of rotation), you can find V as a function of h, then you can find dV/dt as a function of dh/dt and find the function so that dh/dt is also constant. In its full generality, this is a "Calculus of Variations" problem but you are probably expected to guess a simple shape and then show it is correct.
     
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