Problem $1-$ Open Channel Flow $(25$ Points$)$

A rectangular channel $)=(0\mathrm{.}012$ with bottom width of $10\mathrm{.}0ft$ is to carry water at a flow rate of $390f\frac{t^3}{s}$ on a slope of $0\mathrm{.}5\%.$

$Q=390\frac{f}{s},n=0\mathrm{.}012,S_3=0\mathrm{.}005,$ find $y_n$

$($a$)$ Calculate the normal depth for this channel $[5$ Points$].$

$($b$)$ Calculate the Froude number under uniform flow conditions $[5$ Points$].$

$($c$)$ Calculate the critical depth? $[5$ Points$].$

$($d$)$ Is a hydraulic jump possible downstream of a location where the depth was measured to be approximately equal to the normal depth $($i$.$e$.y=y_n)?$ If so$,$ what is the depth after the jump and the energy lost in the jump? $[5$ Points$].$

$($e$)$ Using your calculated values for normal depth and critical depth, classify the water surface profile $($e$.$g$.$ M$2)$ if $y=3\mathrm{.}2ft.$ Be sure to show your work to justify your classification $[5$ Points$].$

Mannings: $V=\frac{K}{n}{R}_n^{0\mathrm{.}67}{S}^{0\mathrm{.}5}A{R}^{\frac{2}{3}}=\frac{Q_n}{K{S}_0^{12}},=2\mathrm{.}94=y^2$