Problem $4(70$ pts$)$: During the field trip, we observed the flow in the manmade rectangle concretes open channel $)=(0\mathrm{.}013$ passing the gate over $9\mathrm{.}5$:$1$ slope first, then $3$:$1$ slope, and adverse $30$:$4$ slope to reach the retention pond as shown in the Figure below. When the flow rate per width $(\frac{Q}{b})$ is $50f\frac{t^2}{s},$ and the velocity of the water at the bottom of the point $1is20\mathrm{.}0f\frac{t}{s},$ conditions will produce a hydraulic jump after the point $2,$ and the depth in the channel at point $3(y_3)$ is increased to be $5ft.$

$1.)$ Determine the water depth at point $1($y$1)$ and find the critical depth before the jump.

$2.)$ Find water depth at point $2($y$2)$ just before hydraulic jump

$3.)$ What type of water surface profile between points $1$ and $2,$ determine the distance between point $1$ and $2$ using direct step method

$4.)$ determine energy loss between point $1$ to $2$ and point $2$ to $3$ in feet.

$5.)$ determine water depth $($y$0)$ just before the gate if the head losses over the $9$:$5$:$1$ slope and $3$:$1$ slope channel is $10$ ft of water