How do you I calculate the Laminar Boundary Layer Y in meters

[firestarter7]

Homework Statement

How do you I calculate the Laminar Boundary Layer Y in meters with Blasius Equation?
I have an expression for U (m/s) and u/U and u(m/s) and also eta=0.1, 0.2...5.2. I am wondering how one could calculate the y laminar boundary layer (m), the y buffer boundary layer (m), the ln y and the y turbulent boundary layer (m)... I know that I need different expression to calculate these...can someone tell me what expressions and how I get the y laminar/buffer/ln y/y turbulent?

This is an example of the sheet I have:
U (m/s) u/U u (m/s) Eta y lam (m) y buff (m) ln y y turb (m)
252.7 0 0 0 ? ? ? ?
252.7 0.047 11.8 0.1 ? ? ?
252.7 0.0939 23.728 0.2 ? ? ? ?
etc...

Homework Equations

I do think I can use the equation

Eta= y*sqrt(U/nu*x)
for ylaminar...but I have already found the tabulated data for Eta from Rosenhead's book in Laminar Boundary Layers...and I have the following X values:
X=...
25.91
27.27
28.94
30.08
32.64
34.62
36.19
39.13
41.99
43.44
44.57
45
44.57
43.44
41.99
39.13
36.19
34.62
32.64
30.88
28.94
27.27
25.91

The following Eta values
h
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2
2.2
2.4
2.6
2.8
3
3.2
3.4
3.6
3.8
4
4.2
4.4
4.6
4.8
5
5.2

and U=252.7 m/s and u/U accordingly.

The Attempt at a Solution

For ylaminar do I only solve for y in the equation Eta= y*sqrt(U/nu*x)?
If so, how what are the expressions for ybuffer, ln y (meaning which y should I take the log function on, the laminar, buffer or turbulent) and yturbulent? Can anyone pls help me? I am unsure about how to see when the transition starts so I can go from ylaminar to ybuffer/ turbulent based on my y values...I am grateful if anyone can help me. Thanks

 

[KataKoniK]

I understand your confusion and I am happy to help you with this problem. First, let's review the basics of boundary layers.

A boundary layer is a thin layer of fluid that forms near a solid surface, where the fluid velocity is affected by the friction between the fluid and the surface. In laminar flow, the fluid particles move in smooth, parallel layers, while in turbulent flow, the fluid particles move in a chaotic, random manner.

Now, to calculate the laminar boundary layer thickness (ylaminar), we can use the Blasius equation you mentioned: Eta = y*sqrt(U/nu*x), where Eta is the dimensionless distance from the leading edge, U is the free stream velocity, nu is the kinematic viscosity, and x is the distance along the surface.

To solve for ylaminar, we can rearrange the equation to y = Eta/sqrt(U/nu*x). Now, in your case, you have tabulated data for Eta and x, and you know U and nu. So you can simply plug in the values and solve for y.

For the buffer layer (ybuffer), we can use the expression ybuffer = 5x, which is a good approximation for most practical cases. This means that the buffer layer thickness is about 5 times the distance along the surface.

To calculate ln y, we first need to determine the transition point from laminar to turbulent flow. This can be done by plotting the Eta values against x and looking for a sudden increase in Eta. Once you have identified the transition point, you can take the natural log of the laminar boundary layer thickness (ln ylaminar) and the buffer layer thickness (ln ybuffer).

Finally, the turbulent boundary layer thickness (yturbulent) can be calculated using the expression yturbulent = 0.37x, which is also a good approximation for most practical cases.

I hope this helps you understand how to calculate the different boundary layer thicknesses using the Blasius equation. If you have any further questions, please don't hesitate to ask. Good luck with your calculations!