STATEMENT OF PROBLEM

Torricelli's Law states that the velocity of water exiting through
a hole is proportional to the square root of 2 g y, where g is
acceleration due to gravity and y is the depth of the water
above the hole.

For small holes, the constant of proportionality
is about 0.6.

We consider three situations.

Situation 1

A cylindrical tank of radius 3 feet and height 8 feet is full of water. A hole of area 1 square inch is punched in the bottom.

How long will it take for the tank to empty?

Situation 2

Instead of the hole, a slit 1/10 of an inch wide is cut in the side of the tank, running vertically from top to bottom.

How long will it take for the tank to empty?

Compare your solutions in Situation 1 and Situation 2.

Situation 3

Can we design a vertical slit of varying width for this tank which
causes the level of water in the tank to drain at a constant rate?