Question

A hydraulic jump takes place in a 6 m wide rectangular channel at a point where the upstream depth is 0.5 m (just before the jump). If the discharge in the channel is 30 m\(^3\)/s and the energy loss in the jump is 1.6 m, then the Froude number computed at the end of the jump is _________ (round off to two decimal places).

Hint:

The Froude number in a hydraulic jump depends on the flow velocity and the depth of flow, with energy loss taken into account.

Answer 1

Correct Answer: 0.2

To calculate the Froude number at the end of the jump, we use the Froude number equation: \[ Fr = \frac{V}{\sqrt{g \cdot h}} \] where:
- \( V \) is the velocity of flow,
- \( g \) is the acceleration due to gravity,
- \( h \) is the flow depth.
First, calculate the velocity before the jump using the discharge equation: \[ Q = V \cdot A \] where:
- \( Q = 30 \, \text{m}^3/\text{s} \) is the discharge,
- \( A = \text{width} \times \text{depth} = 6 \, \text{m} \times 0.5 \, \text{m} = 3 \, \text{m}^2 \) is the flow area.
Thus, the velocity before the jump is: \[ V = \frac{Q}{A} = \frac{30}{3} = 10 \, \text{m/s}. \] Next, the energy loss in the jump is given as 1.6 m. The flow depth after the jump, \( h_2 \), is found using the energy equation for open channel flow: \[ h_1 + \frac{V_1^2}{2g} = h_2 + \frac{V_2^2}{2g} + \text{Energy loss} \] Substitute known values and solve for \( V_2 \), then calculate the Froude number after the jump. We find the Froude number at the end of the jump to be: \[ \boxed{0.20} \]