7.4.2. Virtual Fluid Balls

Now, if you talk about that as is told in many books that when you describe the Lagrangian, where the individual fluid particles will marked it positions, their velocity and these same things, I think I discuss in very beginning is that when you have a n balls should we consider and this would have a different velocity and their directions, okay Va and Vb is the velocity factors can have a different directions, can have a different magnitudes. And can have move any directions, okay but here so that way you have a positions, their positions are changing it, the velocity is changing it, the pressure field is also changing it, that what we can find out to define this the flow descriptions that how the flow varies it, how the velocity varies, how pressure variations are there basically, when you do these in a Lagrangian framework, it is a very easy that mass conservations, and the particle levels, momentum conservations energy we can apply it very easily as compared to the Eulerian framework.

This chunk introduces the concept of virtual fluid balls in the context of fluid mechanics. In the Lagrangian framework, each fluid particle (or virtual fluid ball) can be tracked individually. Each particle has its own position and velocity, which can change over time. This is different from the Eulerian framework where we look at specific points in space without focusing on individual particles. This tracking is important because it allows engineers and scientists to understand how properties like velocity and pressure change over time and space, which is crucial in fluid dynamics.

Imagine a boat on a river (the boat represents a fluid particle). As the boat moves along the river, it encounters different speeds of the water (velocities) and varying depths (pressure). By tracking the boat's journey, you can understand how the river flows around obstacles, how fast it moves, and how its depth changes. This analogy helps visualize how virtual fluid balls operate in tracking fluid motion.

So, if I have a n number of virtual fluid balls are there. And I on to track it, so the each fluid balls are having the velocity and as at the time t, it is having the v velocity at r, it will have a v, there is a change of the velocities having the scalar components. If you try to understand is that I have a, n number of virtual fluid balls are there. And I on to track it, so the each fluid balls are having the velocity and as at the time t, it is having the v velocity at r, it will have a v, there is a change of the velocities having the scalar components.

This chunk emphasizes how virtual fluid balls are utilized in the Lagrangian framework. Here, multiple virtual fluid balls are tracked over time to observe their velocity changes. Each ball has not only its position but also its velocity that can vary based on forces acting on it (like pressure and friction). This kind of tracking allows for a detailed analysis of fluid flow as a dynamic and changing phenomenon, providing insights into how the fluid reacts to various conditions.

Picture a flock of birds flying through the air; each bird is like a virtual fluid ball. Just as each bird can change its direction and speed depending on the wind currents (akin to forces affecting fluid balls), engineers can track these fluid balls to see how they behave under different conditions. This tracking helps in predicting the behavior of fluids in various engineering applications.

So, if you can understand it when you have a kite flying in the sky, there is a vortex shedding just downstream of a kite also, so you can try to understand it or you can try to understand it if a bullet train; the train of more than 300 kilometre per hour is moving with a start speed, we have a triangular shape, it can have a this type of vortex sheddings.

This chunk gives practical examples of vortex shedding in fluid dynamics. When a kite flies, it creates disturbances in the airflow around it, leading to vortices. Similarly, high-speed trains, like a bullet train, face vortex shedding due to their shape and speed. Understanding these phenomena is crucial for engineers to design more efficient systems that minimize drag and improve stability while moving through fluids.

Consider a car driving fast down a road; as it speeds up, the air around it flows over and under, creating whirlpools of air (vortices) behind it. Just like how the car's shape can minimize our wind resistance, engineers use knowledge of virtual fluid balls and vortex shedding to design vehicles that can overcome these air currents efficiently, enhancing performance and fuel efficiency.

I think this considering what sentence is not appropriate. But we can say it is, we are not emphasized what is the force system, more we are oriented to know it what is the descriptions of the motion of the fluid as I demonstrated earlier, the flow fast in triangular cylinders, so we are bothering about how the descriptions of the fluid flows okay, so that is a reason we will talk about now virtual fluid balls, okay that is the way the fluid motions are describing 2 fundamental ways.

This chunk concludes by summarizing the idea of virtual fluid balls as a bridge between understanding fluid motion in both the Lagrangian and Eulerian frameworks. The concept is crucial for grasping the dynamics of fluid flows without placing too much emphasis on the forces involved, thus simplifying the complexity of flow analysis.

Think of virtual fluid balls as the stars in the night sky. Even though we might not understand all their forces and positions without scientific tools, we can observe their paths and motions to predict star movements and map constellations. Similarly, by understanding how these virtual fluid balls move, engineers can better predict how fluids flow and react in various situations.

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