Q$4($a$)$ Compute the normal depth of flow in a river for a discharge of $200\frac{m^3}{s}.$ The river may be approximated to be of a trapezoidal shaped section with the following characteristics: $($a$)$ base width $100m$; $($b$)$ side slope $1$V:$2$H; $($c$)$ Manning's friction factor $0\mathrm{.}02$; $($d$)$ channel longitudinal slope: $0\mathrm{.}001.(8)$

Q$4($b$)$ A rectangular channel of base width $10m$ is carrying a discharge of $20\frac{m^3}{s}.$ If the Manning's friction factor is $0\mathrm{.}01$ and the channel longitudinal slope $0\mathrm{.}0001,$ compute the critical and normal depths. By comparing the two depths, determine whether uniform flow in the channel is sub$-$ or super$-$critical. $(6+2)$

Q$4($c$)$ Explain the terms "Jump rating curve $($JRC$)"$ and "Tailwater rating curve $($TWC$)"$ for the spillway of a dam and the river downstream. Discuss the different types of energy dissipators recommended for the spillway, depending upon the relative position of the two curves. Explain with sketches. $(4)$