7.2. Experimental Setup

Let us start with the experiment setups which we call Hele-Shaw apparatus, okay where we can generate a constant flow and there are the patterns of the colour dye we can inject it, as we injected the colour dye from this; this colour dyes are follows the path lines or the streak lines, as we make the flow in steady, so the stream line and streak line the when you look it, if I put the colour dye, so these what will be show me the streak lines or the path lines, if I tracing on that okay, path line or streak line.

The Hele-Shaw apparatus is an experimental setup used to visualize fluid flow. In this setup, a constant flow of fluid is created, and color dye is injected into the fluid. The path that this dye takes through the fluid reveals how the flow behaves. Depending on whether the flow is steady or unsteady, the lines can represent streamlines, streaklines, or pathlines. Streamlines are the trajectories that fluid particles follow at any given moment in time, whereas streaklines follow fluid particles that have passed a specific point over time.

Imagine blowing bubbles through a straw in a glass of water. The bubbles rise and trace a path through the water. If you were to inject colored dye into the water, it would mix with the bubbles, allowing you to see the routes they take. This visual representation helps you understand how fluids move around objects in their path, just like the bubbles move in the water.

Or since it is a steady flow, I can tell it that it is streamlines, so many of the times we are very much familiarize with the streamlines but when you look it, so what are these lines; is that the streamlines, different colours flow passing over this object, so we can see that how the stream line patterns are happening it, as we change the flow Reynolds numbers this pattern changes it.

In a steady flow, when we inject colored dye, the resulting patterns help visualize the streamlines. These streamlines depict the flow behavior around various objects, showing how different shapes influence fluid movement. As the fluid's Reynolds number changes, which indicates whether the flow is laminar or turbulent, the pattern of the streamlines will also shift. A lower Reynolds number typically results in smoother, more organized flow, whereas higher numbers lead to more chaotic, turbulent flow.

Think about how a smooth river flows around rocks in its path. When the water is calm (low Reynolds number), the flow is predictable, and you can see clear paths. However, during a rainstorm, the river can swell (high Reynolds number), leading to unpredictable flows and turbulent waters. The colored dye in our experiment helps us visualize these differences in flow types just like observing a river during different weather.

So, we can see that how the stream line patterns are happening it, as we change the flow Reynolds numbers this pattern changes it, more we will have a discussions that how the flow past an object we have to describe it.

The patterns of flow around an object are crucial in fluid mechanics. Understanding how the fluid behaves around different shapes helps engineers design objects to minimize drag and maximize efficiency. By studying different flow patterns using the Hele-Shaw apparatus, we can gather data about the forces acting on objects submerged or moving through a fluid. This data is instrumental in applications such as aircraft design, automotive engineering, and even sports.

Consider how the shape of a car affects its speed and fuel efficiency. Sports cars are designed with smooth, aerodynamic shapes that allow air to flow easily over them, reducing drag. This is similar to our experiments with the Hele-Shaw apparatus, where we can see how different shapes influence fluid movements and optimize designs for better performance.

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