Question

In a rectangular channel section, if the critical depth is 2.0 m, the specific energy at critical depth is

1.

 3.0 m

2. 1.33 m
3. 2.5 m
4. 1.5 m

Answer 1

Correct Answer - Option 1 :

 3.0 m

Concept:

Critical Specific Energy:

• The specific energy corresponds to the critical depth of the flow is known as critical specific energy.
• For rectangular channel, it is equal to -

\(E_c = \frac{3}{2}y_c\)

Here,

y_c - critical depth of the flow = \(\left [ \frac{q^2}{g} \right]^{\frac{1}{3}}\)

Here, q - discharge per unit width (m³/s/m)

g - acceleration due to gravity (m/s²)

Calculation:

Given,

Critical depth, y_c = 2.0 m

Hence,

Critical specific energy,

E_c = \(\frac{3}{2}\) × y_c = \(\frac{3}{2}\) × 2 = 3.0 m

• The following table shows the relationship between different types of sections and critical specific energy -

Type of section	Critical specific energy (m)
1. Rectangular	\(\frac{3}{2}y_c\)
2. Triangular	\(\frac{5}{4}y_c\)
3. Parabolic	\(\frac{4}{3}y_c\)

Here,

y_c - critical depth (m)