Q E$1-01$: The flow $Q(\frac{m^3}{s})$ in an open channel is given with the Manning equation

$Q=\frac{1}{n}{A}_c{R}^{\frac{2}{3}}{S}^{\frac{1}{2}}$

where $n=$ Manning roughness coefficient $($a dimensionless number used to parameterize the channel friction$),A_c=$ cross$-$sectional area of the channel $(m^2),S=$ channel slope $($dimensionless$,$ meters drop per meter length$),$ and $R=$ hydraulic radius $($m$),$ which is related to more fundamental parameters by $R=\frac{A_c}{P},$ where $P=$ wetted perimeter $(m).$ For trapezoidal channel as shown

$A_c=By+z{y}^2$ and $P=B+2y\sqrt[\phantom{2}]{1+z^2}$

Given the parameters $n=0\mathrm{.}035,B=10m,z=2,y=3m,$ and $S=0\mathrm{.}003,$ determine discharge $Q$ in the channel by developing an algorithm in Octave.

Write and run the code in octave.