Boundary layer in pipe flow

In summary, the BL thickness for a pipe and parallel plates should be the same for the same free stream velocity. The solution to the slit (parallel plate) problem using the momentum integral method can be found in "Transport Phenomena" by Bird, Stewart, and Lightfoot. The solution for flow over a plate, both the exact Blasius analytical solution and the solution obtained using the momentum integral approximation, can also be found in the same chapter. The solution for the flat plane case will be the same as that for flow in the entry region of a slit and for the entry region of a circular pipe for the very beginning portion of the entry length. However, further downstream within the entry region, the solution will deviate from flat
  • #1
brambram
7
0
Hi

I cannot find an equation for a boundary layer in a pipe flow (laminar). I am looking for an equivalent of the equation δ(x)=4.91x/(√Re) that works for a flow between plates (x is the distance downstream). The thing is- I am looking for BL thickness for still undeveloped flow. I would be very grateful for any help

Best regards
 
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  • #2
brambram said:
Hi

I cannot find an equation for a boundary layer in a pipe flow (laminar). I am looking for an equivalent of the equation δ(x)=4.91x/(√Re) that works for a flow between plates (x is the distance downstream). The thing is- I am looking for BL thickness for still undeveloped flow. I would be very grateful for any help

Best regards

The BL thickness for a pipe should be the same as for parallel plates (for the same free stream velocity) because the BL thickness is small compared to the pipe radius, so, to the BL, the pipe wall looks like a flat plane.
 
  • #3
Dear Chestermiller

Thank you, but I am afraid that my problem tackles pipe with quite small radius. The thing is I need analytical check for CFD simulation, that cannot rely on such a coarse assumption.

Also the function is far from being linear- for the entrance of the pipe that would vitally change the result
 
  • #4
Chestermiller

I actually made a mistake saying that the equation concerns flow between plates- it is flow over a plate. I don't know what is the one for the parallel plates- do you know it? do you think it could be used here? The radius of the pipe is about 10x of the BL thickness.

Thanks again
 
  • #5
brambram said:
Chestermiller

I actually made a mistake saying that the equation concerns flow between plates- it is flow over a plate. I don't know what is the one for the parallel plates- do you know it? do you think it could be used here? The radius of the pipe is about 10x of the BL thickness.

Thanks again

Let me see if I understand you correctly. You solved the fluid flow problem for the hydrodynamic entrance region of a pipe using CFD, and now you are trying to compare the results to the momentum integral approximate solution to the same problem in order to roughly validate your results.

The solution to the slit (parallel plate) problem using the momentum integral method is presented in Transport Phenomena by Bird, Stewart, and Lightfoot, as a problem at the end of one of the early chapters. In the same chapter, they also present the solution for flow over a plate, both the exact Blasius analystical solution as well as the solution obtained using the momentum integral approximation. The solution to the flat plane case is going to be the same as that for flow in the entry region of a slit and for the entry region of a circular pipe for the very beginning portion of the entry length. However, further downstream within the entry region, the solution will deviate from flat plane case. You can apply the very same methodology that Bird et al used for the slit problem to solve the pipe problem. They pretty much lead you through how to do it in the homework problem.

Because, in the problem you are solving, the pipe radius is about 10x the BL thickness (for the total length of pipe you are considering, which is a small fraction of the hydrodynamic entry length), in the CFD solution, you need to have used a non-umiform mesh and need to have packed lots of nodal points near the pipe wall. The situation you are describing is also telling me that the flow-over-a-plate momentum integral solution will be adequate for your purposes, since the boundary layer thickness will not even begin to approach the pipe radius. You need to be thinking in terms of the dimensionless variables, rather than dimensional variables. I can see you have started to do this when you compared the BL thickness to the pipe radius.

Chet
 
  • #6
Thank you! I found this example (slit), but I was not sure if it is a right approximation. But I guess it is the best that I can get- I went on to research on actual velocity profile in the entry stages of flow in a pipe (so 3D), and it turns out that it cannot be described by a single function..

When it comes to the problem outlined in Transport Phenomena, the equation has a ln term, I hope it will be fine to skip it (as δ/radius is low).

Thanks again for the help
 
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  • #7
brambram said:
Thank you! I found this example (slit), but I was not sure if it is a right approximation. But I guess it is the best that I can get- I went on to research on actual velocity profile in the entry stages of flow in a pipe (so 3D), and it turns out that it cannot be described by a single function..

When it comes to the problem outlined in Transport Phenomena, the equation has a ln term, I hope it will be fine to skip it (as δ/radius is low).

Thanks again for the help

No. The ln term is a vital part of the solution. Try expanding the solution in powers of Δ = δ/B and see what you get. (Truncate the expansion at Δ2).
 

1. What is a boundary layer in pipe flow?

The boundary layer in pipe flow is a thin layer of fluid that forms near the surface of a pipe. It is caused by the friction between the fluid and the pipe wall, and it affects the velocity and pressure of the fluid within the pipe.

2. How does the boundary layer affect the flow of fluid in a pipe?

The boundary layer can significantly impact the efficiency of fluid flow in a pipe. It causes a decrease in velocity near the pipe wall, which can result in higher pressure and energy losses. However, it also provides a smooth transition for the fluid to flow from the stationary pipe wall to the faster-moving center of the pipe.

3. What factors influence the thickness of the boundary layer?

The thickness of the boundary layer depends on several factors, including the fluid properties (such as viscosity and density), the pipe diameter, and the fluid velocity. As the fluid velocity increases, the boundary layer becomes thinner.

4. How can the boundary layer be controlled or minimized?

There are several methods for controlling or minimizing the effects of the boundary layer in pipe flow. These include using smoother pipe surfaces, reducing the fluid viscosity, and increasing the pipe diameter. Additionally, using turbulence-promoting devices, such as fins or roughness elements, can help to break up the boundary layer and improve fluid flow.

5. What are the practical applications of understanding the boundary layer in pipe flow?

Understanding the boundary layer in pipe flow is essential in many engineering applications, such as designing efficient piping systems for fluid transport, optimizing heat transfer in heat exchangers, and improving the performance of pumps and turbines. It is also crucial in fields such as aerodynamics and naval architecture, where fluid flow over surfaces plays a significant role.

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