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GATE 2025 AG – Question 46

Soil and Water Conservation Engineering · Fluid Mechanics · 2 marks · Numerical answer

A 90° V-notch has discharge coefficient .6 and water head .49 m. For $g=9.81\,\mathrm{m/s^2}$,find discharge in m³/s, to two decimals.

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Correct answer: 0.21 to 0.29

Explanation

Integrating elemental flow across a triangular notch gives $Q=(8/15)C_d\sqrt{2g}\tan(\theta/2)H^{5/2}$. Here $\tan45^\circ=1$,so $Q=(8/15)(.6)\sqrt{19.62}(.49)^{5/2}=.2382263$ m³/s. Rounded as requested,**0.24 m³/s**.

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