GATE 2024 CE (CE2) – Question 59
A rectangular channel is 4.0 m wide and carries a discharge of 2.0 m$^3$/s with a depth of 0.4 m. The channel transitions to a maximum width contraction at a downstream location, without influencing the upstream flow conditions. The width (in meters) at the maximum contraction is ________________ (rounded off to 2 decimal places).
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 3.51 to 3.55
Explanation
The upstream velocity is $V = \frac{2}{4 \times 0.4} = 1.25$ m/s (subcritical, $Fr = 0.63$). The specific energy is $E = 0.4 + \frac{1.25^2}{2 \times 9.81} = 0.4796$ m. The maximum contraction that does not affect the upstream flow just makes the flow critical in the throat with the same energy: $y_c = \frac{2E}{3} = 0.3197$ m. The critical discharge per unit width is $q_c = \sqrt{gy_c^3} = \sqrt{9.81 \times 0.3197^3} = 0.5662$ m²/s. So the width is $b = \frac{2.0}{0.5662} = 3.53$ m.