Laminar Pipe Flow: Displacement, and Momentum Thicknesses

In summary, Laminar flow in pipes is fully-developed when the boundary layer has penetrated to the center of the pipe. The displacement thickness is R.
  • #1
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Hello. I'm new to the forums. I apologize if I have posted this in the wrong topic area.

I'm new to this hydrodynamics area and I'm trying to learn the concepts of boundary layer thicknesses. My question is about laminar pipe flow and calculating displacement and momentum thicknesses. I was wondering if finding the displacement and momentum thicknesses in a pipe flow is the same as finding them in flow over a flat-plate.

I found the displacement thickness over a flat plate to be:
## \delta_1 = \int_0^\infty (1-\frac{u\rho}{u_{\infty}\rho_{\infty}})dy ##

And the momentum thickness is:
## \delta_2 = \int_0^\infty \frac{\rho u}{\rho_{\infty}u_{\infty}} (1-\frac{u\rho}{u_{\infty}\rho_{\infty}})dy ##

Thank you.
 
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  • #2
In the region where the thicknesses are small compared to the radius of the pipe, you can treat flow in the entrance region to a pipe as flow over a flat plate. However, as the thicknesses become greater, neglect of the curvature becomes less acceptable.

Chet
 
  • #3
Hello Sir,
I just want to know further in this topic that
"Can we calculate displacement thickness for fully developed laminar flow in pipes"
 
  • #4
cabon7969 said:
Hello Sir,
I just want to know further in this topic that
"Can we calculate displacement thickness for fully developed laminar flow in pipes"
For fully developed laminar flow in pipes, the boundary layer has penetrated to the center of the pipe, and the displacement thickness is R.

Chet
 
  • #5
Hello Sir ,
I did not understand how the displacement thickness becomes R.
According to me, displacement thickness is the distance by which streamline get deflected due to effect of boundary layer and also it can be stated as imaginary increase in thickness of wall due to boundary layer.
But for the fully developed laminar flow this thickness will be constant, but i don't know what it will be ?
 
  • #6
For a fully-developed pipe flow, why do you feel the need to define a displacement thickness in the first place? Once the flow is fully-developed, the concept of a boundary layer is somewhat meaningless. There is already a well-defined, well-predicted velocity profile.
 

1. What is laminar pipe flow?

Laminar pipe flow is a type of fluid flow in which the fluid particles move in an orderly, smooth manner in parallel layers, without any mixing or turbulence. It is characterized by a low Reynolds number and is commonly observed in slow-moving or highly viscous fluids.

2. What is displacement thickness in laminar pipe flow?

Displacement thickness is a measure of the thickness of the boundary layer in laminar pipe flow. It is the distance by which the boundary layer would need to be displaced in order to have the same volume flow rate as the actual boundary layer with the same velocity distribution.

3. How is displacement thickness calculated?

Displacement thickness can be calculated using the integral momentum equation, which takes into account the velocity profile and shear stress distribution within the boundary layer.

4. What is momentum thickness in laminar pipe flow?

Momentum thickness is a measure of the average distance by which the momentum of the fluid is reduced due to the presence of the boundary layer. It is related to the thickness of the boundary layer and is also calculated using the integral momentum equation.

5. How does the flow behavior change with increasing Reynolds number in laminar pipe flow?

As the Reynolds number increases in laminar pipe flow, the flow behavior undergoes a transition from laminar to turbulent flow. This is characterized by the appearance of small, chaotic eddies in the flow, resulting in increased mixing and higher drag forces on the fluid. At very high Reynolds numbers, the flow becomes fully turbulent and the velocity profile becomes more uniform.

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