GATE 2024 CE (CE1) – Question 58
A spillway has unit discharge of 7.5 m$^3$/s/m. The flow depth at the downstream horizontal apron is 0.5 m. The tail water depth (in meters) required to form a hydraulic jump is __________ (rounded off to 2 decimal places).
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Correct answer: 4.53 to 4.57
Explanation
The velocity before the jump is $V_1 = \frac{q}{y_1} = \frac{7.5}{0.5} = 15$ m/s and the Froude number is $Fr_1 = \frac{15}{\sqrt{9.81 \times 0.5}} = 6.77$. The sequent (conjugate) depth is $y_2 = \frac{y_1}{2}\left(\sqrt{1 + 8Fr_1^2} - 1\right) = 0.25 \times (\sqrt{1 + 8 \times 45.87} - 1) = 0.25 \times (19.18 - 1) = 4.55$ m. The tail water depth must be this value for the jump to form.