Problem $3.$

A parking lot collected stormwater will be following in a $500m$ long newly excavated channel that is considered to be lined or not with fine gravel and mulch $($subangular stone$)$ with $d_{50}=9mm($part A$)$ or with a more resisting material $d_{50}=25mm($part B$)$ in order to provide dynamic stability of the cross$-$sectional trapezoidal shape. The first channel design parameters with the $d_{50}=9mm$ gives a water depth of $0\mathrm{.}3m,$ bottom width of $2,$ lateral slopes of $3$:$1(H$:$V)$ of $m=3,$ Manning's $n=0\mathrm{.}033$ and channel longitudinal slope of $0\mathrm{.}0049.$ Let $g=9\mathrm{.}81\frac{m}{s^2},$ specific weight of water $=9790\frac{N}{m^3},$ and the specific gravity of the solid material is $2\mathrm{.}65.$ The $d_{50}=25mm$ channel you should compute the Manning's $n$ and the normal depth too. Determine and fill the tables while showing all equations and computations.

$\backslash$table$[[\backslash$table$[[Q(\frac{m^{\text{'}}}{q})=$