$($a$)(10$ pts$)$ Determine the water surface profile of the river $($backwater curve$)$ as it enters the reservoir. How far away from the dam does the river have normal depth?

$($b$)(10$ pts$)$ What would be the annual volume of sediment that would need to be dredged from the reservoir? $($Hint: Compute the average sediment load of the river using the MPM equation before the dam is built and assume all of it will accumulate inside the reservoir$).$

$($c$)(10pts)$ Where will the delta form? $($Hint: Compute the average bed shear stress along the river. Use the energy slope $($not the channel slope$)$ to estimate the shear stresses. Where does the local shear stress drop below the critical shear stress for the material found in the river?$).$