Topic V: Open Channel Flow $(20$ points$)$

Problem $(15)$: water flows at a discharge $(Q)$ in a finished concrete channel of a rectangular cross$-$section with

width $($b$),$ depth $(y),$ and longitudinal slope $(S_0).$

Given the values of $y[m],b[m],$ and $S_0[-],$ calculate the discharge $(Q)$ in $[$Lit$/$s$]$ assuming uniform flow

conditions. Givens: answers:

$y=0\mathrm{.}664m$

$b=3\mathrm{.}264m$

$1$

$139446666i+\frac{1}{5}$

${7276411}^{i\frac{t}{s}}$

Problem $(16)$: water flows in a very wide $($i$.$e$.,$ width $>>$ depth$)$ unfinished concrete channel of a rectangular

cross$-$section with depth $(y)$ and longitudinal slope $(S_0)$ at a discharge per unit width $(q).$

Given the values of $q[\frac{m^2}{s}]$ and $S_0[-],$ calculate the normal flow depth $(y)$ in $cm.$

Given $S^q=4\mathrm{.}644\frac{m}{s}$

$S_0=0\mathrm{.}000135$

answers:

$242453cm3)395\mathrm{.}362cm$

$260\mathrm{.}405cm4)334\mathrm{.}226cm$

Problem $(17)$: water flowing in an open channel of a rectangular cross$-$section with width $($b$)$ transitions from a

mild slope to a steep slope $($i$.$e$.,$ from subcritical to supercritical flow$)$ with normal water depths of $(y_1)$ and

$(y_2),$ respectively.

Given the values of $y_1[m],y_2[m],$ and $b[m],$ calculate the discharge in the channel $(Q)$ in $[$Lit$/$s$].$

Givens:

$g_1=6\mathrm{.}073m,b=1\mathrm{.}33mm$ answers:

$y_3=0\mathrm{.}546m$

${4159\mathrm{.}071}^{\frac{101}{5}}4)7640\mathrm{.}16I^{10\frac{t}{5}}$

Problem $(18)$: a hydraulic jump is formed in an open channel of a rectangular cross$-$section with width $($b$).$

The water depths upstream and downstream of the jump are $(y_1)$ and $(y_2)$ respectively.

Given the values of $y_1[m],y_2[m],$ and $b[m],$ calculate the discharge in the channel $(Q)$ in $Li\frac{t}{s}.$

Givens:

$g_1=0\mathrm{.}342m$

$y_2=7\mathrm{.}033m$

$b=1\mathrm{.}244m$

answers:

$\frac{{11603\mathrm{.}908}^{11+}}{s}$

$\frac{13776\mathrm{.}676111}{5}$

${8299\mathrm{.}474}^{1i\frac{t}{5}}$

$16095\mathrm{.}604li{t}^{\frac{17}{5}}$