GATE 2023 CE (CE1) – Question 60
A hydraulic jump occurs in a 1.0 m wide horizontal, frictionless, rectangular channel, with a pre-jump depth of 0.2 m and a post-jump depth of 1.0 m. The value of g may be taken as 10 m/s$^2$. The values of the specific force at the pre-jump and post-jump sections are same and are equal to (in m$^3$, rounded off to two decimal places) _____________ .
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Correct answer: 0.61 to 0.63
Explanation
The specific force per unit weight is $F = \frac{Q^2}{gA} + A\bar{y}$. The depths $y_1 = 0.2$ m and $y_2 = 1.0$ m are conjugate, so $\frac{y_2}{y_1} = 5 = \frac{1}{2}\left(\sqrt{1 + 8Fr_1^2} - 1\right)$, giving $Fr_1^2 = 15$. Then $V_1^2 = 15 \times 10 \times 0.2 = 30$ and $q = V_1y_1 = 5.477 \times 0.2 = 1.095$ m²/s, with $q^2 = 1.2$. At the pre-jump section $F = \frac{1.2}{10 \times 0.2} + \frac{0.2^2}{2} = 0.6 + 0.02 = 0.62$ m³ (and at the post-jump section, $\frac{1.2}{10} + \frac{1}{2} = 0.62$).