Torricelli’s Law If we punch a hole in a bucket full of water, the fluid drains at a...

Torricelli’s Law If we punch a hole in a bucket full of water, the fluid drains at a rate governed by Torricelli’s law, which states that the rate of change of volume is proportional to the square root of the height of the fluid.

(b) Use the relationship derived in part (a) to find a differential equation for h(t) (that is, you should have an independent variable t, a dependent variable h, and constants in the equation).

(c) Solve this differential equation using separation of variables. It is relatively straightforward to determine time as a function of height, but solving for height as a function of time may be difficult.

(d) Obtain a flowerpot, fill it with water, and watch it drain. At a fixed set of heights, record the time at which the water reaches the height. Compare the results to the differential equation’s solution.

(e) It has been observed that a more accurate differential equation is

Solve this differential equation and compare to the results of part (d).