Chapter 9.3, Problem 49E

Torricelli’s law An open cylindrical tank initially filled with water drains through a hole in the bottom of the tank according to Torricelli’s law (see figure), if h(t) is the depth of water in the tank for t ≥ 0 s, then Torricelli’s law implies $h\text{'}\left(t\right)=-k\sqrt{h}$, where K is a constant that includes g = 9.8 m/s², the radius of the tank, and the radius of the drain. Assume the initial depth of the wafer is h(0) = H m.

1. a. Find the solution of the Initial value problem.
2. b. Find the solution in the case that k = 0.1 and H = 0.5 m.
3. c. In part (b), how long does It take for the tank to drain?
4. d. Graph the solution in part (b) and check that it Is consistent with part (c).