Question

A spillway discharges flood flow at a rate of $9m^3/s$ per metre width. If the depth of flow on the horizontal apron at the toe of the spillway is 46 cm, the tail water depth needed to form a hydraulic jump is approximately given by which of the following options?

• A. 4.90 m
• B. 5.77 m
• C. 6.23 m
• D. 2.54 m

Answer 1

The correct option is B 5.77 m

$q=9m^3/s/m$
and $y_1=46cm=0.46m$
$\therefore V_1=\frac{a}{y_1}=\frac{9}{0.46}=19.565m/s$
$F_1=\frac{V_1}{\sqrt{g{y}_1}}=\frac{19.565}{\sqrt{9.81\times 0.46}}=9.21$
Thus, flow is super-critical.
Thus the sequent depth will be
$\frac{y_2}{y_1}=\frac{1}{2}[-1+\sqrt{1+8F_1^2}]$
$\Rightarrow y_2=\frac{0.46}{2}[-1+\sqrt{1+8\times (9.21{)}^2}]$
$\Rightarrow y_2=0.23\times 25.07$
$\Rightarrow y_2=5.77m$