Question

The flow rate per unit width of a wide rectangular clean-earth channel is 20 m³ s⁻¹ m⁻¹. The calculated critical flow depth in meter will be _____. \(\textit{[Round off to two decimal places]}\)

Hint:

For wide rectangular channels, the critical flow depth can be calculated using the formula involving flow rate and gravity.

Answer 1

Correct Answer: 3.42

The critical flow depth for a wide rectangular channel can be calculated using the formula: \[ d_c = \left( \frac{Q^2}{g} \right)^{1/3} \] where:
- \( d_c \) = critical flow depth (m),
- \( Q \) = flow rate per unit width (m³/s/m),
- \( g \) = acceleration due to gravity (\( 9.81 \, \text{m/s}^2 \)).
Substitute the given values into the formula: \[ d_c = \left( \frac{20^2}{9.81} \right)^{1/3} \] \[ d_c = \left( \frac{400}{9.81} \right)^{1/3} = \left( 40.77 \right)^{1/3} \approx 3.44 \, \text{m}. \] Thus, the critical flow depth is approximately \( \boxed{3.44} \, \text{m} \) (rounded to two decimal places).