Section 4: Soil and Water Conservation Engineering
Fluid Mechanics
Subtopic: Flow in open channels
Question Statement:
A rectangular channel of width $2.0\text{ m}$ carries a discharge of $5.4\text{ m}^3\text{/s}$. Taking $g = 9.81\text{ m/s}^2$, the critical depth of flow $y_c$ in meters is ________ (round off to 2 decimal places).
Answer Key:
0.91
Step-by-Step Solution & Explanation
1. Discharge per unit width $q$:
$q = \frac{Q}{B} = \frac{5.4}{2.0} = 2.70\text{ m}^3\text{/(s}\cdot\text{m)}$
2. Critical depth formula for a rectangular channel:
$y_c = \left(\frac{q^2}{g}\right)^{1/3} = \left(\frac{2.70^2}{9.81}\right)^{1/3} = \left(\frac{7.29}{9.81}\right)^{1/3} = (0.7431)^{1/3} \approx 0.9058\text{ m} \approx 0.91\text{ m}$