Hydraulic Jump in an Open Channel

A hydraulic jump is a phenomenon that occurs in an open channel flow where there is a sudden change in the flow characteristics. It is characterized by a rapid change in the flow velocity and a significant increase in the water depth. This phenomenon is important in various engineering applications such as spillways, sluice gates, and canals.

Statement Analysis

Let's analyze each statement to determine if it is correct or not:

1. When the Froude number is equal to or less than one.
The Froude number (Fr) is a dimensionless parameter that compares the inertia forces to the gravitational forces in an open channel flow. It is defined as the ratio of the flow velocity to the square root of the product of the acceleration due to gravity and the flow depth.

Fr = V / √(gD)

Where V is the flow velocity, g is the acceleration due to gravity, and D is the flow depth.

A hydraulic jump occurs when the Froude number is equal to or less than one. This is because when the Froude number is less than one, the flow is considered subcritical, and when it is equal to one, the flow is at the critical condition. In both cases, the flow undergoes a sudden change due to a discontinuity in the flow regime, leading to a hydraulic jump. Therefore, statement 1 is correct.

2. At the toe of a spillway.
A spillway is a structure built on a dam to control the release of water from a reservoir. The toe of a spillway is the downstream end where the water is discharged.

Hydraulic jumps commonly occur at the toe of a spillway due to the sudden change in flow conditions. As the water flows over the spillway, it gains kinetic energy and then dissipates it in the form of turbulence and increased water depth at the toe. Therefore, statement 2 is correct.

3. Downstream of a sluice gate in a canal.
A sluice gate is a device used to control the flow of water in a canal or a channel. When the sluice gate is opened, it creates a sudden change in flow conditions downstream.

Similar to a spillway, a hydraulic jump can occur downstream of a sluice gate due to the abrupt change in flow characteristics. The flow velocity decreases, and the water depth increases, leading to a hydraulic jump. Therefore, statement 3 is correct.

4. When the bed slope suddenly changes.
The bed slope of an open channel refers to the change in elevation of the channel bed along its length. If the bed slope suddenly changes, it can cause disruptions in the flow, leading to a hydraulic jump.

When the bed slope suddenly decreases, the flow velocity increases, and the water depth decreases, resulting in a supercritical flow condition. Conversely, when the bed slope suddenly increases, the flow velocity decreases, and the water depth increases, leading to a subcritical flow condition. In both cases, a hydraulic jump can occur. Therefore, statement 4 is correct.

Conclusion

Based on the analysis, it can be concluded that statements 2, 3, and 4 are correct. These situations can lead to the occurrence of a hydraulic jump in an open channel. Therefore, the correct answer is option C: 2