Small Reynolds Number Flow around Flat Plate

In summary, the conversation is about a problem involving a semi-infinite plate in the direction of flow. The individual asking the question is not an expert in fluid mechanics and is looking for an expression to determine the thickness of the shaded viscous region at small Reynolds numbers. The fluid being used is argon at 1100 degrees celsius with a kinematic viscosity of 1.6 cm^2/sec and a velocity of 10 cm/s over a square rod of size 0.635x0.635cm and a length of about 10cm. The Reynolds number is expected to range from <1 near the leading edge to ~60 far from the leading edge, making the Blasius solution invalid. The individual is
  • #1
uby
176
0
Hello,

I have a problem I am trying to model analytically (please note: I am NOT a fluid mechanics expert -- I come from a chemistry background):

A semi-infinite plate is oriented axially in the direction of flow.

Please refer to the following page for an illustration of my problem:
http://www.ecourses.ou.edu/cgi-bin/eBook.cgi?doc=&topic=fl&chap_sec=09.3&page=theory

The third picture is the Blasius solution, which does not apply at small Reynolds numbers. I am looking for an expression to tell me the thickness of the shaded viscous region from the top two pictures (i.e. - for small Reynolds numbers!) as function of position from the leading edge.

Any references would be appreciated.

Thanks!
 
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  • #2
What is the fluid, it's velocity and the size of the plate?
 
  • #3
hi RTW:

the fluid is argon at 1100 degrees celsius (kinematic viscosity 1.6 cm^2/sec) , traveling at 10 cm/s over a square rod (0.635x0.635cm, ~10cm length)

based on these values, i expect the reynolds number to vary from < 1 near the leading edge to ~60 far from the leading edge.

the blasius solution is only valid for reynolds numbers greater than about 1000, so i feel safe in assuming that it doesn't apply.
 

1. What is meant by "Small Reynolds Number Flow"?

Small Reynolds Number Flow refers to a type of fluid flow that occurs at low speeds and low viscosity, resulting in a low Reynolds number. The Reynolds number is a dimensionless quantity that represents the ratio of inertial forces to viscous forces in a fluid. In small Reynolds number flow, viscous forces dominate, and the flow appears smooth and laminar.

2. How is the flow around a flat plate affected by the Reynolds number?

The flow around a flat plate is greatly affected by the Reynolds number. At low Reynolds numbers, the flow is laminar and follows a smooth path along the surface of the plate. As the Reynolds number increases, the flow becomes more turbulent and chaotic, resulting in increased drag and a larger wake behind the plate.

3. What is the significance of studying small Reynolds number flow around a flat plate?

Studying small Reynolds number flow around a flat plate is important in understanding the fundamentals of fluid mechanics. This type of flow occurs in many practical applications, such as microfluidics, boundary layer analysis, and low-speed aerodynamics. It also serves as a basis for understanding more complex flow phenomena.

4. How is the drag force affected by small Reynolds number flow around a flat plate?

In small Reynolds number flow, the drag force on a flat plate is primarily due to viscous forces. As the Reynolds number increases and the flow becomes more turbulent, the contribution of pressure drag also increases. This results in an overall increase in drag force on the plate.

5. Are there any limitations to using small Reynolds number flow theory for practical applications?

Yes, there are limitations to using small Reynolds number flow theory for practical applications. This type of flow is only applicable to low-speed and low-viscosity fluids, and it does not accurately predict the behavior of high-speed or turbulent flows. Additionally, the assumptions made in small Reynolds number flow theory may not hold true in all real-world scenarios.

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