Calculate the normal depth in a rectangular channel with a bottom width of $10$ m $,$ Manning's roughness $n=0\mathrm{.}010$ and a longitudinal slope of $S_0=0\mathrm{.}0001.$ Given the discharge in the channel changes is $100\frac{m^3}{s}.($Use the Newton$-$Raphson method and the table provided below to show your calculation for one iteration$)$

$\backslash$table$[[$Iteration$,y_i(m),a_i(\frac{m^3}{s}),f(y_i),f^{\text{'}}(y_i),y_{i+1}$