If we punch a hole in the bottom of a cylinder with water in it, the height of the water will decrease faster at the beginning that towards the end. This is because the pressure on the bottom decreases when the water level decreases. A little more precise:
The speed at which water flows out of a container is proportional to the height:. V′(t)=−kh where V(t) is the volume of the water in the vase, h is the height from the hole up to the water level and k is a constant. V′(t) may well be given in liters per second. Now imagine that you are going to turn a vase that is such that the height decreases with constant speed when you make a small hole in the bottom. What shape must that vase have?
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