GATE 2024 CE (CE2) – Question 35
A 2 m wide rectangular channel is carrying a discharge of 30 m$^3$/s at a bed slope of 1 in 300. Assuming the energy correction factor as 1.1 and acceleration due to gravity as 10 m/s$^2$, the critical depth of flow (in meters) is _____________ (rounded off to 2 decimal places).
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Correct answer: 2.90 to 2.92
Explanation
The discharge per unit width is $q = \frac{30}{2} = 15$ m²/s. With the energy correction factor, the critical flow condition is $y_c = \left(\frac{\alpha q^2}{g}\right)^{1/3} = \left(\frac{1.1 \times 225}{10}\right)^{1/3} = 24.75^{1/3} = 2.91$ m. The bed slope does not enter the critical depth.