Given the following data for a $50-$year storm, estimate the peak rate of flow to a culvert entrance. Consider the rainfall intensity$-$duration$-$frequency curves of Figure $7\mathrm{.}7$ applicable. The contributing upstream drainage area is $45$ acres. The overland flow distance is $180$ feet and the average land slope is $2\mathrm{.}5\%.$ The land use of the overland flow portion of the drainage area is lawns, sandy soil. The land use for the drainage basin is $75\%$ residential, single$-$family units and $25\%$ lawns, sandy soil with an overall average slope of about $2\mathrm{.}7\%.$ A channel leading to the culvert is $1900$ feet long with a slope of $0\mathrm{.}012$ ft$/$ft$.$ The grassed channel is trapezoidal with a bottom width of $5$ feet and side slopes of $2$ feet vertical to $1$ feet horizontal.