3. Rapidly Varied Flow

So now we start with rapidly varied flow and then it is almost to the end, but we will start with some concept of the rapidly varied flow. So, you see the figure here and what do you notice? See, if you see, there is something that is coming with a velocity V here and somehow this height is larger, I mean, this seems that there is something which is different from this area, so the velocity becomes V2, maybe the height has increased or there is a bump or something. So, in that case, the flow becomes, so it varies very rapidly. Suddenly, if there is something, the rapid change in the water level elevation or some water level elevation, it is called rapidly varied flow. In this particular case, this there is a hydraulic jump due to the change in bottom elevation. We are able to source, we are able to say that because we know it from before. This is the photograph from probably one of the experiments.

Rapidly varied flow is a term used in hydraulic engineering to describe scenarios where the water flow experiences sudden changes in velocities and elevations. This means that as water moves through a channel, various factors can cause abrupt changes, such as a change in channel width or slope. One classic example of rapidly varied flow is a hydraulic jump, where water flowing with high velocity suddenly slows down and increases in height due to a shift in channel conditions. This concept plays a crucial role in understanding how water behaves in different environments and conditions. Hydraulic jumps often indicate turbulence and energy loss in the flow.

Imagine a river flowing smoothly over a flat area suddenly encountering a waterfall or a sudden drop in elevation. When this happens, the water cannot maintain its speed and starts to pile up or become turbulent at the edge of the drop—this is similar to a hydraulic jump. Just like how the water slows down and splashes at the edge, rapidly varied flow exhibits dynamic changes in velocity and height due to obstacles or changes in slope.

One; if you see a flow like this, if there is a flow coming in this direction and the area suddenly increases that is the rapidly varied flow that happens due to the transition. So, first was due to the height, the second one was due to the, this one is due to the transition, so changing the area, transitioning from smaller area to larger area, for example.

Rapidly varied flow can occur due to two main factors: changes in height and changes in the cross-sectional area of the flow. When water flows through a narrower section (like a pipe) and then enters a larger section, it can experience rapid variations in speed and height—as the area increases, the velocity decreases and the elevation may rise. This transition point causes turbulence and a significant change in flow characteristics, leading to a hydraulic jump or other abrupt flow dynamics.

Think of a garden hose that narrows down, leading to a faster spray of water from the nozzle. When you then remove the nozzle and let the water flow into a bucket with a wider opening, the speed decreases while the water level in the bucket rises quickly. This scenario mimics the transition from a small area to a larger area and illustrates how water can experience rapidly varied flow as it adjusts to the new conditions.

So, now, the most famous type of rapidly varied flow is called hydraulic jump. So, this is the concept that becomes the core of our next 2 lectures and we will start the next lecture and with this particular concept, hydraulic jump, go through a small derivation and solve some problems which will give you a better understanding of hydraulic jump. So, this is all for now. I will see you in the next lecture. Thank you.

The hydraulic jump is a key phenomenon within the study of rapidly varied flow. It highlights how fluid dynamics can change dramatically under certain conditions, making it an essential topic for engineers and scientists working with water flow. Understanding hydraulic jumps involves studying changes in kinetic and potential energy, as well as how they impact flow stability and efficiency in channels. Through derivations and problem-solving, the next lectures will aim to deepen our understanding of these dynamics.

Picture a water fountain where water shoots into the air. As the water reaches a certain height, it slows down and spreads out instead of shooting back down immediately. This action resembles a hydraulic jump, where energy is dissipated, and airflow patterns change, giving us an exciting visual representation of rapidly varied flow.

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