$($a$)$ A river having rectangular cross$-$section $125m$ wide and $6\mathrm{.}00m$ deep has a bed slope of $1$ in $4000.$ The bed of the river consists of fine sand of $0\mathrm{.}25mm$ diameter, and the bed roughness $k_s$ can be taken as $0\mathrm{.}45mm.$ The vertical velocity distribution at the vertical centre line of the river is given by $\frac{u}{u_0}=2\mathrm{.}5ln(30\frac{y}{k}s).$ The sediment density is$2650k\frac{g}{m^3}$ and viscosity of water $=1\mathrm{.}14{10}^{-3}k\frac{g}{m}-s.$Estimate the total suspended sediment discharge based on the relationship $q_s=Cuy,$ where $q_s$ is the transport rate per unit width. Use

Rouse equation to find $C.$