PROBLEM $19$

In HW$2,$ Problem $14,$ you calculated the water depth after the gate, and the water depth after

the hydraulic jump. a$)$ Let's assume that $y_{\text{u}\text{p}\text{s}\text{t}\text{r}\text{e}\text{a}\text{m}}$ remains at $10ft$ and the specific discharge

is still $20f\frac{t^2}{s},$ but the tailwater reduces to $4\mathrm{.}8ft.$ Please calculate the new $y_{\text{I}}$ for a condition

of free discharge from the gate. b$)$ What happens in between the contraction of the flow and

the new $y_l?$ c$)$ Now, please consider that the tailwater increases slowly from the value of $y_2.$

Using the plot for the discharge coefficient for a gate, please calculate the discharge for two

values of $y_2,$ keeping the same $y_l$ of part a$)$