GATE 2025 CE (CE1) – Question 62
A 5.0 m wide rectangular channel carries a discharge of 10 m$^3$/s at a depth of 1.5 m under uniform flow. To produce critical flow conditions without affecting the upstream conditions, the channel bottom elevation should be raised (in m) by __________________ (*rounded off to 2 decimal places*).
Assume that there is no loss of head at the raise, kinetic energy correction factor is 1.0, and acceleration due to gravity is 9.81 m/s$^2$.
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Correct answer: 0.47 to 0.49
Explanation
The upstream specific energy is $E_1 = 1.5 + \frac{V^2}{2g}$ with $V = \frac{10}{5 \times 1.5} = 1.333$ m/s, so $E_1 = 1.5 + 0.0906 = 1.5906$ m. For critical flow at the raised bed, $q = 2$ m$^2$/s, $y_c = \left(\frac{q^2}{g}\right)^{1/3} = 0.7415$ m and $E_c = 1.5y_c = 1.1123$ m. With no energy loss the bed can be raised by $E_1 - E_c = 1.5906 - 1.1123 = 0.48$ m.