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A rectangular open channel of 6 m width is carrying a discharge of 20 m^3/s. Taking acceleration due to gravity as 9.81 m/s^2 and assuming water to be incompressible and inviscid, the depth of flow at which the specific energy of the flowing water is minimum for the given discharge is

1. 0.82 m
2. 1.04 m
3. 2.56 m
4. 3.18 m

Correct answer: 1.04 m

Solution

For minimum specific energy in a rectangular channel, the flow is critical. The discharge per unit width is \(q = Q/b = 20/6 = 3.333\,\text{m}^2/\text{s}\). Using \(y_c = (q^2/g)^{1/3}\), we get \(y_c \approx (11.11/9.81)^{1/3} \approx 1.04\,\text{m}\).

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