Ancient Water Clock Simulation
The clepsydra ("water thief") is one of humanity's oldest timekeeping devices, used from ancient Egypt to medieval Europe. Water drains from an upper vessel through a small orifice into a lower vessel. A float in the lower vessel rises with the collected water, driving a pointer along a graduated scale to indicate elapsed time. The fundamental physics is governed by Torricelli's law: the exit velocity of fluid through an orifice depends on the square root of the water height above it. This means a cylindrical vessel drains non-linearly — the flow slows as the water level drops. Ancient engineers discovered that a specific conical shape (wider at top, narrower at bottom) compensates for this effect, producing a nearly linear flow and thus a uniform timescale.