GATE 2017 CE (CE2) – Question 56
A 1 m wide rectangular channel carries 2 m³/s. For the same specific energy, the subcritical depth is twice the supercritical depth. The subcritical depth, to two decimals, is ______ m.
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Correct answer: 1.06 to 1.08
Explanation
Unit discharge is $q=Q/b=2$ m²/s. Let the shallow depth be a and deep depth 2a. Equal specific energy gives $a+q^2/(2ga^2)=2a+q^2/(8ga^2)$, hence $a^3=3q^2/(8g)$. Deep depth is $2[3(4)/(8\times9.81)]^{1/3}=1.06948$ m, or 1.07 m.