Q$1$:

$($b$)$: A rectangular concrete channel of dimensions $2$ m wide carries a liquid at a depth of $1\mathrm{.}25$ m down a slope of $1/800.$ The liquid has a dynamic viscosity $0\mathrm{.}02$ Pas and relative density $($R$.$D$.)$ of $0\mathrm{.}8.$ The absolute roughness $\backslash (\backslash$varepsilon $\backslash )$ can be taken to be $0\mathrm{.}1$ mm $.$ Using the D'Arcy$-$Weisbach method, Calculate the:

I. Area of flow

II$.$ Wetted Perimeter

III. Equivalent diameter

IV$.$ Relative roughness, $\backslash (\backslash$varepsilon$\_\{\backslash$mathrm$\{$R$\}\}\backslash )$

V$.$ Initial Reynolds number using an initial trial velocity value of $\backslash (2\mathrm{.}0\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash )("$Trial $1")$

VI$.$ Friction factor based on the Reynolds number obtained in $($v$)("$Trial $1")$

VII. Initial trial flow velocity $("$Trial $1")$

VIII. 'New' Reynolds number using the velocity obtained in $($vii$)("$Trial $2")$

IX$.$ 'New' Friction factor based on Reynolds number obtained in $($viii$)("$Trial $2")$

X$.$ 'New' flow velocity $("$Trial $2")$