QUESTION $2[25$ MARKS$]$

$($a$)$ A trapezoidal channel has a channel width of $7\mathrm{.}5m,$ side slope of $z=2,$ bottom slope of

$0\mathrm{.}0015,$ and Manning's coefficient of $0\mathrm{.}025,$ carries a discharge of $15\frac{m^3}{s}.$

i$)$ Compute the normal and critical depths using the algebraic method.

$[8$ Marks$]$

ii$)$ Construct the Specific Energy Diagram $($SED$)$ and determnine the alternate depth when

$E=1\mathrm{.}75Ec.$

$[10$ Marks$]$

iii$)$ Estimate the maximum rise $z$ allowable given the same discharge, channel witdh and

bottom slope if the initial condition is stated as in $($a$)$ ii$).$

$[7$ Marks$]$