Derivation of the shape of a clepsydra

[jakncoke]

Homework Statement

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.

Homework Equations

Torricelli Law

The Attempt at a Solution

No clue.

 

[HallsofIvy]

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.