2. Distortion of Fluid Particle

The fluid particle retains its original shape in the uniform flow outside the boundary layer. That is very true, because outside the boundary layer there are no effects and the fluid particle, this is the fluid particle above the boundary layer, this is the fluid particle that is going to be in the boundary layer. So, when it moves in this direction, there is no problem at all because all the points will have equal velocities.

In the region outside the boundary layer, fluid particles move smoothly without any disturbances and thus maintain their original shape. Since every point in this area is experiencing similar velocities, the fluid moves uniformly. This uniform flow is essential for understanding how the characteristics of the fluid change when it enters the boundary layer.

Imagine a group of people walking perfectly in sync on a smooth, straight path; they all maintain their individual shapes while moving together. This scenario reflects how fluid particles behave in uniform flow before they encounter any obstacles.

However, this particle here, after entering the boundary layer the particles begin to distort, as you can see. This is where it starts distorting and when it goes it distorts more, it distorts more, depending upon what the velocity gradient but there is definitely is a distortion from this point to this point, as soon as it enters the boundary layer.

Once a fluid particle enters the boundary layer, it starts to experience varying velocities across its body due to the presence of a velocity gradient. The part of the particle closer to the solid surface moves slower than the part further away, resulting in the distortion of its shape as it flows through this region. This distortion is a critical aspect of fluid behavior in boundary layers.

Think of a flag fluttering in the wind. When it's held away from a wall (analogous to the boundary layer), it stays flat. But when it nears the wall, the wind hits it unevenly, causing it to ripple and distort. This illustrates how fluid particles are distorted as they encounter the boundary layer.

So, the why this distortion occurs? This distortion occurs due to the velocity gradient inside the boundary layer. How? Because the top of the particle has a larger velocity than its bottom. So, this point here, the bottom will have lesser velocity than at the top because this is more closer to the solid surface.

The distortion of fluid particles arises from the velocity differences within the boundary layer. The upper section of a fluid particle experiences a higher velocity while the lower section, which is nearer to the surface, moves slower due to friction. This differential movement leads to a rotation of the fluid particle, producing what is known as vorticity, contributing to the overall rotational nature of flow in the boundary layer.

Imagine a spinning soccer ball. If you were to press down on one side with your hand, that side would move slower than the other, causing the ball to tilt. Similarly, the top and bottom of the fluid particle experience different velocities, resulting in distortion and rotation.

Now, we are going to see, what the boundary layer thickness is. In real sense, physically, there is no sharp edge to the boundary layer. Now, the boundary layer thickness is the distance from the plate at which the fluid velocity is within some arbitrary value of the free stream velocity.

The boundary layer thickness is defined as the distance from a flat plate where the fluid's velocity equals a certain percentage of the free stream velocity, typically considered to be around 99%. This thickness indicates the region in which the effects of viscosity and friction are significant compared to the rest of the fluid beyond this layer, which experiences uniform flow.

Think of a sponge placed in water. The part of the sponge that is wet represents the boundary layer, where water has penetrated and interacts with the sponge's surface. Beyond this, the water remains unaffected, similar to how the fluid moves uniformly beyond the boundary layer.

Some of the definitions is displacement thickness, given by, delta star, very important term, in this particular module of hydraulic engineering. This is another thing called momentum thickness that is called theta. And then there is something called energy thickness which is given by, delta double star.

In boundary layer analysis, three important thickness measures are defined: displacement thickness (δ*), momentum thickness (θ), and energy thickness (δ**). Each of these parameters provides different insights into the effects of the boundary layer on flow characteristics, helping engineers and scientists understand and quantify fluid behavior in various contexts.

You can think of these thicknesses like different layers in a cake. Just as each layer adds its own unique flavor and texture to the cake, these thicknesses each represent different aspects of the flow within the boundary layer, helping us understand the overall performance of the fluid in a system.

So, within the boundary layer there is a velocity deficit. So, this is the boundary layer. So, U capital U is the uniform velocity profile, here also the free stream velocity is the same. But say, at this distance if the velocity is u, then the deficit of the velocity that is, happening is U minus u.

Within the boundary layer, fluid velocity is lower compared to the free stream velocity due to the effects of viscosity and friction. This difference, known as velocity deficit, means that the actual fluid velocity (u) is less than the free stream velocity (U), which ultimately affects flow rates and other dynamic properties of the fluid.

Imagine a car moving on a highway (free stream) versus driving in a tight traffic jam (boundary layer). In the jam, the car moves much slower than the speed limit on the highway, representing the velocity deficit.

Suppose what happens, if the plate, my question to you is, what happens if the plate is displaced at section a - a by an amount delta dash? So, here, this delta dash is called the displacement thickness.

Displacement thickness is a theoretical concept used to understand how much a plate would need to be displaced to account for the velocity deficit in the fluid. If a plate were to shift, the effective area through which fluid flows would be altered, illustrating the impact of the boundary layer on flow dynamics.

Imagine you're trying to swim in a crowded pool. To move efficiently, you would need to displace some of the people (much like the displacement thickness) to create a path for yourself. This concept helps visualize how the boundary layer affects flow and movement.

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