15.1.5. Disturbances in Flow

If you have these things and if you create any disturbance okay let me there is a one big stone is there. okay or just dump a stone here. It creates a disturbance to these flow systems okay or you throw a stone to a river. So it creates the disturbance. Once it creates the disturbance, how does it propagate it because there is a off streams and the down streams okay.

When a disturbance occurs in an open channel flow, such as throwing a stone into a river, it alters the flow dynamics in that area. This disturbance affects how the flow moves both upstream and downstream. Understanding how these disturbances propagate is crucial in fluid mechanics as it helps explain the behavior of water flow in various conditions.

Imagine tossing a pebble into a calm pond. The ripples expand outward from the point of impact, moving in all directions. Similarly, when an object disrupts a river's flow, it generates waves that travel upstream and downstream, altering how the water moves in those directions.

Because of this disturbance what is the wave speed the speed of surface water wave okay surface water wave. So that means if I put it a very simple way this is what hypothetically we are creating a disturbance wave okay. If you consider is that there is a open channel flow is going on and we create a disturbance because by putting a stone as you create a disturbance that is what will be reflected on the surface that means we are talking about the surface disturbance what is happening it.

The speed of the surface water wave generated by a disturbance is vital in understanding how the flow will respond. This speed dictates whether the disturbance will influence upstream or downstream flow conditions. The relationship between the flow regime and this wave speed describes behaviors in different flow conditions, like subcritical and supercritical flow.

Think of waves formed when a speedboat suddenly accelerates on a lake. The faster the boat, the faster the waves travel away from it. If the boat speeds faster than the wave created, the boat's wake influences only the water behind it (downstream), illustrating the influence of wave speed on water movement.

If you look at that we talk about 3 types of the flow subcritical, critical and supercritical. In terms of the flow crowd numbers we define as if a lesser than 1 that means the gravity force is more than the inertia forces with this the case we define as subcritical flow okay. When you have a very rare occurs it that you will have the inertia force is equal to the gravity forces of the flow systems that we call the critical flow. if a flow crowd numbers is greater than 1 we call supercritical flow.

Flow types can be categorized as subcritical, critical, and supercritical using Froude numbers, which compare gravitational forces to inertial forces within the flow. For example, in subcritical flow (Froude number < 1), gravitational forces dominate, while in supercritical flow (Froude number > 1), inertia forces take precedence. Critical flow happens when these forces balance.

Imagine a river flowing gently (subcritical flow), where you can easily see reflections on the water's surface. If a sudden surge occurs (like during a storm), it transforms the calm flow into a rapid current (supercritical flow). The shift from gentle ripples to powerful waves illustrates the concept of flow transitioning through these three conditions.

The low velocity the flow crowd number lesser than that small disturbance travels off streams affects the off streams conditions at the high velocity when flow crowd number get small difference cannot travel the off streams thus the off stream conditions cannot be influenced by the downstream conditions.

At low velocities, disturbances can travel upstream and downstream, affecting flow conditions in both directions. However, at high flow velocities (specifically in supercritical flows), disturbances are unable to travel upstream effectively. This understanding is crucial for predicting how changes in one part of a channel can impact the rest of the flow system.

Picture a train moving through a station. When it travels slowly, passengers can get on and off easily. However, when the train speeds up, passengers can no longer get on easily or influence how the train continues on its journey. This reflects how disturbances can impact flow in different ways depending on its speed.

If the conditions when this velocity is a lesser than speed of the surface water wave which we have derived is a functions of the flow depth square root of the flow depth that times we have subcritical flow. The critical flow is the condition there is very special conditions where the velocity is equal to the speed of surface wave.

The condition for critical flow occurs when the flow velocity equals the speed of the surface wave. This balance represents a unique state in fluid dynamics, where both gravitational and inertial forces are equal. In simpler terms, hitting this threshold of flow velocity allows for a stable yet dynamic flow state.

Think about riding a bicycle down a slope. At a very controlled speed, you're able to balance between speeding up and slowing down. But if you pedal too hard or slow down too much, you could wobble or lose control. Similarly, achieving critical flow means being in that flow sweet spot where everything runs smoothly without being too fast or too slow.

So very simple things. It is very simple things as we learn from the Bernoulli's equations as we learn from the pipe flow the same concept we are putting it with a assumptions is that these are no doubt as I said it very very flat conditions when you construct a canal when you constructed the natural rivers are very flats okay except in some of the waterfalls and all.

Understanding disturbances in flow is vital for predicting how systems behave under various conditions. Using principles from fluid mechanics, particularly those derived from Bernoulli's equations, we can analyze flow in open channels effectively. It’s important to remember that these principles hold best in relatively flat channels.

Consider a road trip through a flat landscape. Knowing the terrain helps you gauge how your vehicle will navigate smoothly without unexpected stops or bumps. Similarly, understanding how water flows along open channels helps engineers design better systems to manage and utilize this flow effectively.

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