GATE 2026 CE (CE2) – Question 55
The flow depth for a discharge of 10 m$^3$/s in a wide rectangular channel is 2.0 m. Assume that the flow is uniform.
If the discharge is doubled, the flow depth (in m) in this channel is _________ (*rounded off to two decimal places*).
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Show answer and explanation
Correct answer: 3.01 to 3.05
Explanation
For uniform flow in a wide rectangular channel the hydraulic radius is the depth, so by Manning's equation the discharge is proportional to $y^{5/3}$. Doubling the discharge gives $\left(\frac{y_2}{y_1}\right)^{5/3} = 2$, so $y_2 = 2.0 \times 2^{3/5} = 2.0 \times 1.5157 = 3.03$ m.