Correct Answer - Option 1 : 1.51 m
Concept:
Hydraulic jump: When the flow conditions change form supercritical (Fr > 1) to subcritical (Fr < 1), this results to an abrupt rise of water accompanied by turbulent rollers is called as hydraulic Jump.
For a rectangular frictionless channel, both depths are related as:
\(\frac{{{{\rm{y}}_2}}}{{{{\rm{y}}_1}}} = \frac{1}{2}\left[ {\sqrt {1 + 8{{\rm{F}}_1}^2} - 1} \right]\)
Where y2 = post jump depth, y1 = pre jump depth and F1 = Froude number before jump
Froude number \(= \sqrt {\frac{{{{\rm{Q}}^2}{\rm{T}}}}{{{\rm{g}}{{\rm{A}}^3}}}}\)
Where, Q = discharge, T = top width, g = acceleration due to gravity and A = area of flow
Calculation:
y1 = 0.4 m
v1 = 6m/sec
B = 5 m
\(\begin{array}{l} {F_{r1}} = \frac{{{V_1}}}{{\sqrt {g{y_1}} }} = \frac{6}{{\sqrt {10 \times 0.4} }} = 3\\ \frac{{{y_2}}}{{{y_1}}} = \frac{1}{2}\left[ {\sqrt {1 + 8F_{r1}^2 - 1} } \right]\\ {y_2} = \frac{{0.4}}{2}\left[ {\sqrt {1 + 8 \times {3^2} - 1} } \right] = 1.51 \end{array}\)
