Chapter 1, Problem 6PS

Water Height For a bathtub with a rectangular base, $\text{Toricelli's}$ Law implies that the height $h$ of water in the tub $t$ seconds after it begins draining is given by

$h={\left(\sqrt{h_{\text{o}}-\frac{2\pi d^2\sqrt{3}}{lw}}t\right)}^2$

where $l$ and $w$ are the tub’s length and width, $d$ is the diameter of the drain, and $h_{\text{o}}$ is the water’s initial height. (All measurements are in inches.) You completely fill a tub with water. The tub is $60$ inches long by 30 inches wide by $25$ inches high and has a drain with a two-inch diameter

(a) Find the time it takes for the tub to go from being full to half-full.

(b) Find the time it takes for the tub to go from being half-full to empty.

(c) Based on your results in parts $\left(\text{a}\right)$ and $\left(\text{b}\right)$, what general statement can you make about the speed at which the water drains?