3.2. Significance of 0.99 Free Stream Velocity

Now, we will talk about another phenomenon, that is, distortion of a fluid particle within the boundary layer. What happens? So, this figure has been taken from Munson Young and Okiishi’s Fundamentals of Fluid Mechanics published by Wiley and Sons. So, let me just, so, what it says is that 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. 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.

As a fluid particle flows over a surface, it maintains its original shape outside the boundary layer because the flow is uniform. However, once the particle enters the boundary layer, it experiences distortion due to varying velocities within this region. This distortion occurs because fluid particles near the surface experience different speeds compared to those further away. The consequence of this velocity difference is that the shape of the fluid particle changes as it moves deeper into the boundary layer, becoming more and more distorted.

Imagine a group of runners on a track. If the track is perfectly straight (like flow outside a boundary layer), all runners remain in their lanes and maintain their formation. But if the track curves (like entering the boundary layer), runners on the inner curve slow down more than those on the outer curve, causing some to veer off course or distort their formation. This analogy illustrates how fluid particles can distort when subjected to varying flow velocities.

So, 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. So, this is an important term, boundary layer thickness delta. We have seen similar term in some slides before. And what is this boundary layer thickness? It is distance from the plate, the flat plate over which we have considered the flow. So, distance from the plate at which the fluid velocity is within some arbitrary value of the free stream velocity. Ideally, at the top of this boundary layer, the velocity should be equal to the free stream velocity, normally, at the top. So, this is the boundary layer. So, because of this is the velocity is going to be zero and at one point we have to consider where the boundary layer. And so we assume, when the velocity reaches almost 99% of free stream velocity, the boundary layers cease to exist above that. And that thickness is called the boundary layer thickness.

Boundary layer thickness refers to the vertical distance above a flat plate where the flow velocity is close to the free stream velocity. It is crucial for understanding how fluid behaves near surfaces. When fluid flows over a flat surface, right next to the surface, the velocity is nearly zero due to friction. As you move away from the surface, the velocity increases and eventually approaches the free stream velocity. The significance of 99% free stream velocity is that we consider the boundary layer to end when the flow velocity reaches this point, simplifying analysis in fluid dynamics.

Picture a swimmer diving into a pool. Close to the surface (the wall), the water feels still (velocity near zero), but as they dive deeper, they feel less resistance and can swim faster (velocity approaching the free stream velocity). When they reach a certain depth, they no longer feel much of that surface friction, similar to how fluid flows freely once it leaves the boundary layer.

Now, what is so special about 0.99? Why not for 0.96 or 0.98? To remove this confusion, we will now look at some of the definitions. 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. So, these 3 are very important terms in boundary layer analysis.

The choice of 0.99 as the standard threshold for defining the end of the boundary layer is somewhat arbitrary but serves practical purposes in fluid mechanics. It provides a consistent point for analysis. Additionally, related terms such as displacement thickness, momentum thickness, and energy thickness help describe how the flow behaves within and beyond the boundary layer. Each of these thicknesses has specific definitions and implications for understanding fluid flow.

Think of 0.99 as the finish line for a race. Just as runners cross the finish line at different speeds but are recognized as having completed the race once they reach the mark, fluid particles are understood to be outside the boundary layer once they achieve a speed close to the free stream velocity. The associated thicknesses guide engineers in managing flow effectively, just like race strategists plan their athletes' paths.

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