GATE 2022 CE (CE1) – Question 58
Depth of water flowing in a 3 m wide rectangular channel is 2 m. The channel carries a discharge of 12 m3/s. Take g = 9.8 m/s2. The bed width (in m) at contraction, which just causes the critical flow, is _________ without changing the upstream water level. (round off to two decimal places)
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Correct answer: 2.14 to 2.16
Explanation
Upstream velocity is $12/(3\times2)=2$ m/s and specific energy is $E=2+2^2/(2\times9.8)=2.204082$ m. At the just-critical contraction, $E=3y_c/2$, so $y_c=1.469388$ m.
Critical discharge satisfies $Q=b_c\sqrt{gy_c^3}$, giving $b_c=12/\sqrt{9.8(1.469388)^3}=2.1523$ m. Rounded, **2.15 m**.