The water clock (clepsydra) shown in Fig. P3.101 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 \(5 \mathrm{~cm} / \mathrm{hr}\) if the drain hole is \(1.5 \mathrm{~mm}\) in diameter. What size container ( \(h\) and \(R_{0}\) ) permits the clock to run for \(24 \mathrm{hr}\) without refilling?

Figure P3.101

Transcribed Image Text:

-Ro Water level -R(z) 1