Flow Characteristics Before and After a Hydraulic Jump

Before we delve into the flow characteristics before and after a hydraulic jump, let's first understand what a hydraulic jump is. A hydraulic jump occurs when there is a sudden change in the flow regime of a fluid, typically from supercritical flow to subcritical flow. This phenomenon is commonly observed in open channel flow, such as rivers, canals, and spillways.

Specific Forces and Specific Energies

To understand the flow characteristics before and after a hydraulic jump, we need to consider two important parameters: specific forces and specific energies.

- Specific Forces: Specific force is defined as the force per unit weight of the fluid. It represents the resistance of the fluid to flow. In open channel flow, specific force is given by the equation: F = V^2/g + z, where F is the specific force, V is the velocity of the fluid, g is the acceleration due to gravity, and z is the elevation of the fluid surface above a reference plane.

- Specific Energies: Specific energy is defined as the sum of the elevation head and the velocity head of the fluid. It represents the total energy per unit weight of the fluid. In open channel flow, specific energy is given by the equation: E = V^2/2g + z, where E is the specific energy, V is the velocity of the fluid, g is the acceleration due to gravity, and z is the elevation of the fluid surface above a reference plane.

Flow Characteristics Before a Hydraulic Jump

Before a hydraulic jump occurs, the flow is characterized by supercritical flow, where the velocity of the fluid is greater than the wave velocity. In this case:

- The specific forces are equal: Since the specific force depends on the velocity and elevation of the fluid surface, and these parameters remain constant before the hydraulic jump, the specific forces before the jump are equal.
- The specific energies are unequal: The specific energy is a combination of the velocity head and elevation head. Before the hydraulic jump, the velocity is high, resulting in a larger velocity head and hence a higher specific energy.

Flow Characteristics After a Hydraulic Jump

After a hydraulic jump, the flow transitions from supercritical flow to subcritical flow. In this case:

- The specific forces are unequal: As the flow transitions from supercritical to subcritical, the velocity decreases significantly. This results in a decrease in the specific force, as the force per unit weight of the fluid is reduced.
- The specific energies are equal: During a hydraulic jump, a significant amount of energy is dissipated. This energy is converted into heat and turbulence. As a result, the specific energy after the jump is equalized, as the energy is redistributed within the flow.

Conclusion

In conclusion, the flow characteristics before and after a hydraulic jump are such that the specific forces are equal, but the specific energies are unequal. This is because the specific force is determined by the velocity and elevation, which remain constant before the jump, while the specific energy is influenced by the velocity head, which is higher before the jump due to the higher velocity.