$4\mathrm{.}6\mathrm{.}70$ The water clock $($clepsydra$)$ shown in Fig. P$4\mathrm{.}6\mathrm{.}70$ is an ancient device for measuring time by the falling water level in a large glass container. The water slowly drains out through a small hole in the bottom. Determine the approximate shape $R(z)$ of a container of circular cross section required for the water level to fall at a constant rate of $5c\frac{m}{h}r$ if the drain hole is $1\mathrm{.}5$ mm in diameter. What size container $(h$ and $R_0)$ permits the clock to run for $24$ hr without refilling?

HIGUREP