QUESTION $2(20$ marks$)$

$($a$)$ What is a spillway? List any three $(3)$ essential requirements of a

spillway design. $[4mks]$

$($b$)$ With the aid of well$-$illustrated sketches, briefly explain the working

principles of any $3$ of the following types of spillways: $($i$)$ Ogee spillway

$($ii$)$ Siphon spillway $($iii$)$ Side channel spillway $($iv$)$ Chute spillway. $[6$mks$]$

$($c$)$ An ogee spillway with vertical upstream face has the following data.

i$.$ Discharge design: $300\frac{m^3}{s}$

ii$.$ Crest length: $150m$

iii. Normal reservoir level: $700m$

iv$.$ Average river bed level: $650m$

v$.$ Coefficient of discharge: $2\mathrm{.}2$

vi$.$ Take $K_p$ and $K_a$ as; $0\mathrm{.}01$ and $0\mathrm{.}1$ respectively

Determine the crest level and the downstream profile of the overflow spillway