A drainage canal is to be dug to keep a low-lying area from flooding during heavy rains. The canal would carry the water to a river that is 1 mile away and $6 \mathrm{ft}$ lower in elevation. The canal will be lined with cast concrete and will have a semicircular cross section. If it is sized to drain all of the water falling on a $1 \mathrm{mile}^{2}$ area during a rainfall of $4 \mathrm{in} . / \mathrm{h}$, what should the diameter of the semicircle be?