Question Bank • QB_SWCE_FM_007 NAT • 2 Marks

Section 4: Soil and Water Conservation Engineering

Fluid Mechanics

Subtopic: Flow in open channels

Question Statement:

In a rectangular horizontal open channel, a hydraulic jump is formed where the initial upstream flow depth is $y_1 = 0.25\text{ m}$ and the upstream Froude number is $F_{r1} = 4.0$. The sequent depth of flow $y_2$ downstream of the jump in metres is ________ (round off to 2 decimal places).

Answer Key:

1.29

Step-by-Step Solution & Explanation

From Belanger's momentum equation for a hydraulic jump in a rectangular channel: $y_2 = \frac{y_1}{2} \left( \sqrt{1 + 8 F_{r1}^2} - 1 \right)$ Given: • $y_1 = 0.25\text{ m}$ • $F_{r1} = 4.0 \implies F_{r1}^2 = 16$ $1 + 8(16) = 1 + 128 = 129$ $\sqrt{129} \approx 11.3578$ $y_2 = \frac{0.25}{2} (11.3578 - 1) = 0.125 \times 10.3578 = 1.2947\text{ m} \approx 1.29\text{ m}$
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