16.2.4. Flow Depth and Velocity Variations

The basic idea to know it, the flow depth variations in open channels, the velocity variations, how the velocity changes it, how much of energy losses, okay. losses is happening it because of the flow and mostly it is governed by the gravity forces and the frictional forces as I discussed earlier. So we have just two force component the gravity force and frictional force component.

In open channel flow, two main factors influence how water flows: depth and velocity. When the depth of the flow changes, the speed of the flow also changes. This relationship is largely driven by gravity, which pulls the water downhill, and friction, which slows it down as it moves along the channel. Hence, as water flows over a surface, its height (depth) and speed (velocity) are continuously adjusting to balance these forces.

Imagine a slide at a playground. If the slide is steep (higher depth), children will go down quickly (high velocity). If the slide is less steep (lower depth), they will go down slowly (lower velocity). Similarly, in open channels, the relationship between depth and velocity affects how fast water flows.

When you have a subcritical flow, okay as we discuss more details subcritical flow that means when you have a flow proud number lesser than 1. When you throw a stone to a reverse we have a subcritical flow the wave will be propagates the both upstream as well the downstreams.

Flow can be categorized into three types based on the Froude number, a dimensionless value that compares the flow velocity to the wave speed. Subcritical flow occurs when this number is less than 1, meaning the flow is slower than the surface wave. In this case, disturbances in the water can travel upstream as well as downstream, allowing waves created (for example, by throwing a stone) to affect both directions.

Think of standing in a calm river. If you drop a rock, the ripples will move both upstream and downstream. This is similar to subcritical flow: the water moves slowly, and disturbances can travel in both directions. Now, if the flow were very fast (supercritical), like a strong current, the disturbances would only move downstream.

Hydraulic jumps create a lot of turbulent structures and energy losses happen it when flow goes through the supercritical to subcritical.

A hydraulic jump occurs when water flows from an area of higher velocity (supercritical flow) to lower velocity (subcritical flow). This transition often creates turbulence and energy losses due to the sudden change in flow conditions. The turbulence can be evident as bubbles and churned water, which also indicates energy being dissipated.

Picture a waterfall where fast-moving water suddenly drops into a calmer pool below. The rapid falling water (like supercritical flow) hits the still water and creates a splash (the hydraulic jump). This splash creates turbulence and noise, reflecting the energy loss as the water transition occurs.

If I know the upstream conditions, I can just simple way write it it is a jump like this okay it is a jump part here again I am writing a cross section 111 so just to you to coming back to the book levels which is given in the pre-off streams will have the 11 and downstream will be 22.

To analyze hydraulic jumps, we look at the flow conditions both upstream and downstream of the jump. The jump is typically modeled as a transition from one state (high energy and velocity) to another (lower energy). By measuring conditions before and after the jump, we can calculate how much energy has been lost in the form of turbulence and heat, helping engineers design better hydraulic systems.

Envision a water slide that ends with a splash pool: before the slide ends, the water rushes fast (upstream conditions). Once it hits the splash pool, it slows down dramatically (downstream conditions), splashing water everywhere. Engineers analyze how much water splashes out to understand the energy losses that occur during this transition.

The same concept we will talk about and more details I will today talk how we can use a specific energy which is a graphical representations of energy versus the flow depth of a channel cross section where the datum is considered is a channel bottoms more or less the horizontal channel slopes.

Specific energy is a concept that describes the relationship between the energy of flowing water and its depth. It can be graphically represented, allowing us to visualize how energy varies with changes in depth. The channel bottom acts as a baseline reference point (datum), and as we plot energy against depth, we can identify critical points where flow conditions change significantly.

Imagine a graph that tracks how high a ball bounces when thrown into different depths of water. The graph would show different energy levels depending on the depth of water, similar to how specific energy curves illustrate the relationship between energy and water depth in channels. It helps engineers understand how different depths will affect the energy of a water flow.

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