In$-$Class Exercise $($Work in trios$)$

Costa Rica generates more than $95\%$ of its electricity from renewable sources.

Approximately $75\%$ comes from hydropower. To further lower its dependency on

fossil$-$fuels down to $0\%,$ the Costa Rican Institute of Electricity is studying a site along

the Ayil River to build a new hydropower plant.

The Ayil River has a mean annual discharge of $91\frac{m^3}{s}$ and a slope of $0\mathrm{.}00033$ within

the reach of interest. The cross$-$section of the river is $11m$ wide and relatively

rectangular in shape. The bed of the river is covered in gravel with a median grain

size $D_{50}2\mathrm{.}5mm$ and density ${}_s=2,600k\frac{g}{m^3}.$ Use the Manning$-$Strickler relation

to determine Manning's $n.$

As part of the feasibility studies and preliminary design tasks, you have been hired

to determine the distance away from the proposed $10m$ high dam where sediment

entering the reservoir will deposit and form a delta. This location will help them design

road access for future dredging operations. You also need to estimate the annual

volume of sediment that will accumulate there so they can plan the future dredging

efforts.

$($a$)$ 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?

Use the Direct Step Method covered in class.

$($b$)$ 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$)$ 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?$).$