Allied & ICAR Exam Bank • ALLIED_1153 NAT • 2 Marks

Section 4: Soil and Water Conservation Engineering

Open Channel Flow

Subtopic: Critical Flow

Question Statement:

A rectangular drainage channel of width $B = 3.0\text{ m}$ carries a discharge $Q = 9.0\text{ m}^3/\text{s}$. Taking acceleration due to gravity $g = 9.81\text{ m/s}^2$, the critical depth of flow $y_c$ (in m) is:

Answer Key:

0.97

Step-by-Step Solution & Explanation

Discharge per unit width $q = \frac{Q}{B} = \frac{9.0}{3.0} = 3.0\text{ m}^2/\text{s}$. Critical depth $y_c = \left(\frac{q^2}{g}\right)^{1/3} = \left(\frac{3.0^2}{9.81}\right)^{1/3} = \left(\frac{9.0}{9.81}\right)^{1/3} = (0.9174)^{1/3} \approx 0.9717\text{ m}$.
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