A wide rectangular channel has a sluice gate to regulate the flow. When the approach flow from upstream is $70\frac{m^3}{s},$ the water depth just upstream of the gate is $6$ m $.$

$($a$)$ What is the opening of the sluice gate?

$($b$)$ If there are blocks to form a hydraulic jump with a downstream pool depth of $3$ m $,$ what is the total force of the blocks?

$($c$)$ What are the energy losses across the hydraulic jump for $($b$)?$

$($d$)$ If there are no blocks in place and a hydraulic jump is formed downstream of the gate, what is the pool level?

$($e$)$ What are the energy losses across the jump in $($d$)?$

$($f$)$ Explain why energy losses are different in $($C$)$ and $($e$)?.$