I came across this last night and thought to seek some input.
A 12 hour water clock has a height of 4 feet and a radius (at the top) or 1 foot. The shape is a parabola rotated about the y-axis. What should be the function of the curve and the radius of the hole so the water level will fall at a constant rate?
I'm interested in the original problem, but more in the relationship between the water level and the rate of water exiting the clock.
Here's my dilemma: As the water level falls in the container, the pressure on the water exiting the hole will lessen. So, I assume there would be an inverse relationship between the water level and the rate of water leaving the parabaloid. I then assume that there will be an infinite number of disks of water of height dh. the disks would be A=pi*r^2. But what would govern rate of water exiting the tank?
I did do some research on water clocks and found a LOT of really interesting devices many ancient countries used just by manipulating water in this way!