Q$1$

Consider a smooth and wide rectangular channel with a unit$-$width discharge $q=2\mathrm{.}044\frac{m^2}{s},$ a normal

depth $y_n=1\mathrm{.}067m$ and bed slope $S_o=0\mathrm{.}0005.$ If the water level is raised to a depth $y_o=3\mathrm{.}048m,$

calculate the backwater profile using the gradually varied flow equation

$\frac{dy}{dx}=S_o\frac{1-(\frac{y_n}{y}{)}^{\frac{10}{3}}}{1-(\frac{y_c}{y}{)}^3}$

$($Hints: use the table below$)$