Question

The Froude number of flow in a rectangular channel is 0.8. If the depth of flow is 1.5 m, the critical depth is

1. 1.80 m
2. 1.56 m
3. 1.36 m
4. 1.29 m

Answer 1

Correct Answer - Option 4 : 1.29 m

Concept:

Froude number (F) for a rectangular channel is given by,

\(F= \frac{V}{{\sqrt {9.81 × y} }}\)

Where,

V = Velocity of flow through the rectangular channel

y = Depth of flow

Critical depth of flow y_c is given by

\({{\rm{y}}_{\rm{c}}} = {\left( {\frac{{{q^2}}}{g}} \right)^{\frac{1}{3}}}\)

​q = discharge per unit width

\(q = \frac{Q}{b} = \frac{{V × A}}{b} = \frac{{V × y × b}}{b}\)

∴ q = V × y

​​Calculation:

Given:

F = 0.8, y = 1.5 m​​

\(0.8 = \frac{V}{{\sqrt {9.81 × 1.5} }}\)

V = 3.07 m/s

q = 3.07 × 1.5 = 4.6 m³/s/m

\({y_c} = {\left( {\frac{{{4.6^2}}}{9.81}} \right)^{\frac{1}{3}}}\)

∴ y_c = 1.29 m