A 50-ft-long aluminum gutter (Manning coefficient \(n=0.011\) ) on a section of a roof is to handle a flowrate of \(0.15 \mathrm{ft}^{3} / \mathrm{s}\) during a heavy rainstorm. The cross section of the gutter is shown in Fig. P10.70. Determine the vertical distance that this gutter must be pitched (i.e., the difference in elevation between the two ends of the gutter) so that the water does not overflow the gutter. Assume uniform depth channel flow.

Figure P10.70

5 in. 3 in. 60