3. A water clock is an axisymmetric vessel with a small exit hole of radius a in the bottom; see the figure below.

(a) Find the vessel shape for which the water level falls equal heights in equal intervals of time. (b) What was the main assumption you made in deriving your solution? (c) If you took your clock to an alien planet with a gravitational potential given by Phig ∞ z² would your clock still function?