A lined rectangular concrete drainage channel is $10\mathrm{.}0$ m wide and carries a flow of $8$

m$3/$s$.$ In order to pass the flow under a roadway, the channel is contracted to a width of $6$

m$.$ Under design conditions, the depth of flow just upstream of the contraction is $1\mathrm{.}00$ m$,$

and the contraction takes place over a distance of $7$ m$.($a$)$ If the energy loss in the

contraction is equal to V$1$

$2/2$g $,$ where V$1$ is the average velocity upstream of the

contraction, what is the depth of flow in the constriction? $($b$)$ Does consideration of

energy losses have a significant effect on the depth of flow in the constriction? $($c$)$ If the

width of the constriction is reduced to $4\mathrm{.}50$ m and a flow of $8\mathrm{.}0$ m$3/$s is maintained,

determine the depth of flow within the constriction $($include energy losses$).($d$)$ If

reducing the width of the constriction to $4\mathrm{.}50$ m influences the upstream depth, determine

the new upstream depth