$2.$ HYDRAULIC MODELING: STANDARD STEP METHOD $($HEC$-$RAS$)$

For the compound channel with a discharge of $\backslash (200\backslash$mathrm$\{$~m$\}^\{3\}/\backslash$mathrm$\{$s$\}\backslash ),$ the water surface elevation at the upstream station is at El $100$ m $.$ The next station is $500$ m downstream. Using the expansion and contraction coefficients of $0\mathrm{.}3$ and $0\mathrm{.}1$ respectively. determine the water surface elevation at the downstream station. Use the standard method for gradually varied flow $($HEC$-$RAS manual computations$).$ Use at least six significant digits in your computations.

a$.$ Compute the conveyance factors $\backslash (\backslash$mathrm$\{$K$\}\backslash$left$(\backslash$mathrm$\{$AR$\}^\{2/3\}/\backslash$mathrm$\{$n$\}\backslash$right$)\backslash )$ for each section of the upstream station. Determine the average velocity $\backslash (\backslash$mathrm$\{$V$\}\backslash$left$(\backslash$mathrm$\{$Q$\}/\backslash$mathrm$\{$A$\}\_\{\backslash$text $\{$tot $\}\}\backslash$right$)\backslash ),$ friction slope $\backslash (\backslash$mathrm$\{$S$\}\_\{\backslash$mathrm$\{$f$\}\}\backslash )$ and kinetic energy correction factor $\backslash (\backslash$alpha $\backslash )$ at the upstream station.

b$.$ Using a trial value of $\backslash (\backslash$mathrm$\{$WSE$\}=\backslash$mathrm$\{$El$\}99\mathrm{.}99\backslash$mathrm$\{$~m$\}\backslash )$ at the downstream station, compute the conveyance factors $\backslash (\backslash$mathrm$\{$K$\}\backslash$left$(\backslash$mathrm$\{$AR$\}^\{2/3\}/\backslash$mathrm$\{$n$\}\backslash$right$)\backslash )$ for each section of the upstream station. Determine the friction slope $\backslash (\backslash$mathrm$\{$S$\}\_\{\backslash$mathrm$\{$f$\}\}\backslash )$ and the kinetic energy correction factor $\backslash (\backslash$alpha $\backslash )$ at the downstream station.

c$.$ Based on the results of a$.$ and b$.,$ compute the headloss due to friction and the expansion$/$contraction loss.

d$.$ Using the energy equation, compute the water surface elevation $($WSE$)$ at the downstream station. Compare the result with the trial value. If the difference between the values is within $1$ cm $,$ the computed value from the energy equation is the correct WSE at the downstream station.