$6\mathrm{.}8\mathrm{.}13.$ A diversion gate backs up flow in a $5-$ft wide rectangular irrigation channel $(S_0=0\mathrm{.}001,n=0\mathrm{.}015).$ The

discharge in the channel is $50cfs.$ If the depth of flow at the gate is $3\mathrm{.}5ft,$ determine the channel and flow classification

$($e$.$g$.,$ M$-2,$ S$-1,$ etc.$)$ upstream of the gate and explain your supporting logic. Then determine the water surface profile by

finding the depth of flow at distances of $100,300,$ and $600ft$ upstream of the gate. Use a spreadsheet or appropriate

computer software to perform the computations. $($See the book's preface for computer softwa re suggestions.$)$ ANSWER IS M$-1,3\mathrm{.}45$ft$,3\mathrm{.}35$ ft$,$ and $3\mathrm{.}22$ ft