GATE 2026 CE (CE2) – Question 52
Width (in m) of a rectangular channel required to carry a discharge of 96 m$^3$/s at a critical depth of 9.8 m is _____ (*rounded off to two decimal places*).
Use acceleration due to gravity = 9.8 m/s$^2$
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Correct answer: 0.99 to 1.01
Explanation
For a rectangular channel the critical depth is $y_c = \left(\frac{q^2}{g}\right)^{1/3}$, so $q^2 = g\,y_c^3 = 9.8 \times 9.8^3 = 9.8^4$ and $q = 9.8^2 = 96.04$ m$^2$/s per metre of width. The width is $B = \frac{Q}{q} = \frac{96}{96.04} = 1.00$ m.