A $10$ m wide rectangular channel carries $16\mathrm{.}0$ m $3/$s and has a roughness coefficient of $0\mathrm{.}015$ and a slope of $0\mathrm{.}0016.$ If a $5$ m

high dam is placed across the channel raising the water depth to $5\mathrm{.}70$ m at a location $5\mathrm{.}0$ m upstream from the dam,

determine the channel and flow classification $($e$.$g$.,$ M $2,$ S $1,$ etc.$)$ and explain your supporting logic. Then determine the

water surface profile upstream from the control section $($where the depth is $5\mathrm{.}70$ m$)$ by finding the depth of flow at

distances of $200,600,1,500,$ and $3,000$ m upstream. Use a spreadsheet program or appropriate computer software to

perform the computations.