Water at $20C(=998\mathrm{.}2\frac{kg}{m^3})$ is flowing in a rectangular channel $5m$ wide at a

normal depth of $3m$ with rough concrete pavements. The channel is running

on a slope of $0\mathrm{.}0005$ and carries a discharge of $22\mathrm{.}5\frac{m^3}{s}.$ The representative

roughness element of the bed material is $0\mathrm{.}01m.$

$($a$)$ Determine the Chezy $C$ value and Darcy $f$ for this channel.

$($b$)$ Compute the values of the shear stress and shear velocity imparted to the

channel boundary.

$($c$)$ Using the velocity equation with representative bed element as $lon,$ compute

the velocity profile for this condition.

$($d$)$ Using the velocity obtained at a distance of $2\mathrm{.}5m$ from the bed as $v_m,$

compute the velocity profile by the $\frac{1}{7}$ power law and compare with the

results from part $($c$).$