 So, the next thing that von Karman did after coming up with the quadratic velocity profile in his momentum integral technique was he went ahead and evaluated the boundary layer thickness and he used the relations that he got out of the control volume analysis for both the wall friction as well as the drag on the plate. And so he combined those two together and enabled him to get the boundary layer thickness. That's what we're going to take a look at in this segment. So, what von Karman did is he had this relationship for the momentum thickness, and this one for his quadratic velocity profile subject to the boundary conditions we talked about in the last segment. He plugged that profile into the momentum thickness and was able to come up with this relationship here. And we will refer to this as being equation A. And he also had a relationship for the wall shear stress. And from that, he could obtain this for the wall shear stress. And that would have been using the velocity profile that he had obtained. Now, also from the control volume analysis, he had the following. And so using the expression from A, and this is equation D, and then he combines those two, and we will call this equation E. Now what he did is he had this expression for shear stress. And if we look back here, he had this expression for shear stress. So, he equated those two. So, rearranging, he was able to come up with this relationship here. And what he then did is he integrated that. And knowing that the boundary layer thickness was zero at x equals zero. So, he used the boundary condition in order to get the constant of integration. And rearranging and taking the square root, he obtained this relationship here, where that is under the square root sign. And that was the relationship that he obtained for the thickness of the boundary layer as a function of x. And one thing that we can look at is this term in here. And that is a slightly familiar term to us. And that is basically one over the Reynolds number, because we have the kinematic viscosity in the numerator there. So, that can also be written as delta over x. So, the boundary layer thickness divided by stream-wise position along the plate is approximately equal to 5.5 divided by rex. Remember, that's the way that we write the boundary, or the Reynolds number for a boundary layer, raised to the power of one half. And so, that's another way of writing the expression that von Karman obtained for the thickness of the boundary layers. So, that was a very powerful advancement that had occurred in fluid mechanics when he derived this. However, I should make the caveat that this was done subject to an assumed velocity profile, the quadratic profile. And consequently, this is not a perfect solution, but it was one that helped them quite a bit. And it was actually pretty close to the actual boundary layer thickness growth rate for a laminar boundary layer. So, what we're going to do in the next segment is we're going to take a look at the skin friction. Now, that's another thing that von Karman was able to calculate using his momentum integral technique.