Chapter 1, Problem 1.30P

Consider the milk container of Example 1.4.2 (Figure 1.4.7). A straw 19 cm long was inserted in the side of the container. While adjusting the tap flow to keep the water height constant, the time for the outflow to fill a 250-ml cup was measured. This was repeated for several heights. The data are given in the following table.

$\begin{array}{llllllllllll}\text{Height }\left(\text{cm}\right)\hfill & 11\hfill & 10\hfill & 9\hfill & 8\hfill & 7\hfill & 6\hfill & 5\hfill & 4\hfill & 3\hfill & 2\hfill & 1\hfill \\ \text{Time }\left(\text{s}\right)\hfill & 7\hfill & 7\hfill & 7\hfill & 8\hfill & 9\hfill & 10\hfill & 11\hfill & 13\hfill & 15\hfill & 17\hfill & 23\hfill \end{array}$

Obtain a functional description of the volume outflow rate f through the straw as a function of water height h above the hole.

Figure 1.4.7 An experiment to determine flow rate versus liquid height.