Section 4: Soil and Water Conservation Engineering
Fluid Mechanics
Subtopic: Flow in open channels
Question Statement:
A rectangular irrigation flume of width $3.0\text{ m}$ carries a total water discharge of $12.0\text{ m}^3\text{/s}$. Taking acceleration due to gravity $g = 9.81\text{ m/s}^2$, the critical depth of flow in metres is ________ (round off to 2 decimal places).
Answer Key:
1.18
Step-by-Step Solution & Explanation
1. Discharge per unit width ($q$):
$q = \frac{Q}{B} = \frac{12.0\text{ m}^3\text{/s}}{3.0\text{ m}} = 4.0\text{ m}^2\text{/s}$
2. Critical depth ($y_c$) in a rectangular open channel:
$y_c = \left( \frac{q^2}{g} \right)^{1/3} = \left( \frac{4.0^2}{9.81} \right)^{1/3} = \left( \frac{16.0}{9.81} \right)^{1/3} = (1.63099)^{1/3} \approx 1.177\text{ m} \approx 1.18\text{ m}$