16.4.1. Formation of Hydraulic Jumps

Let us come back to the hydraulic jumps, how does it form? If you look at it, if you have more or less a horizontal surface and you have a sluice gate. The flow is coming from this side, it has a depth. After that, you can see that the flow will be like a jet flow.

A hydraulic jump occurs when water flowing in an open channel transitions from a supercritical state (high speed) to a subcritical state (lower speed). This often happens downstream of a sluice gate where the water initially flows rapidly like a jet due to a sudden change in channel depth or slope. The transition leads to significant turbulence and a sudden increase in flow depth.

Think of a water fountain where the water shoots high into the air (supercritical flow) before it falls back into a pool below (subcritical flow). The moment it hits the water pool, you observe splashes and turbulence, resembling a hydraulic jump.

So we can see that typically it will have a jet type of flow... if this is the v1 velocity and this is the v2 velocity... So we have a v1 y1 is equal to v2 y2.

In this scenario, the mass conservation principle applies, meaning the mass inflow must equal the mass outflow. For incompressible flows, this translates to the relationship that the product of the velocity and the depth of flow at two different points must be the same. Therefore, v1 times y1 (upstream flow) equals v2 times y2 (downstream flow) which helps us understand how velocity and depth are interrelated.

Imagine a garden hose: when you partially cover the opening with your thumb, the water shoots out faster (higher velocity) and the hose's opening area decreases (similar to the depth of flow). Here, the volume of water being pushed remains constant, but its speed changes, illustrating the same principle.

As the velocity increases, does it go to supercritical levels or not? ... the flow is changing from supercritical to subcritical regions.

As water transitions from supercritical flow (flow with a Froude number greater than 1) to subcritical flow (Froude number less than 1), a hydraulic jump forms. This transition is characterized by a rapid change in flow depth and velocity, often accompanied by turbulent mixing and energy dissipation, leading to a jump in the water surface.

Picture throwing a rock into a still pond: the splash created when it hits the water is akin to a hydraulic jump. The rock (representing supercritical flow) hits the water's surface, causing a turbulence (hydraulic jump) that spreads outward.

Hydraulic jumps create a lot of turbulent structures... energy losses happen when flow transitions from supercritical to subcritical.

When a hydraulic jump occurs, significant energy loss results, primarily because of turbulence created in the water. This means that the energy that was previously used to maintain a high-speed flow is dissipated during the transition, which can be a critical factor in designing channels and structures downstream.

Think of a roller coaster: when you go over a high peak and down into a dip, you rapidly lose speed due to the energy required to go back up. Similarly, water loses energy as it transitions from a high-speed flow to a slower, deeper flow, resulting in turbulence—much like the splashing of water at the bottom of the roller coaster dip.

If I know the upstream conditions... we can compute the energy losses... E1 is equal to E2 plus hL.

To analyze hydraulic jumps, we can use conservation of energy principles along with previously discussed relationships involving flow depth and velocity. By knowing the flow conditions upstream (E1) and downstream (E2), we can calculate the energy losses (hL) that occur during the jump. This is essential for designing effective hydraulic structures.

This analysis is like budgeting—if you know how much money you have at the start (E1) and how much you need to spend (E2), you can determine how much you are losing (hL) during your expenditures to effectively plan for your finances.

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