Question about the Reynolds number and fluid drag

In summary, the conversation discusses the concept of drag in fluid dynamics and how it can be applied in scenarios involving a fluid encased in a solid container. The question of whether the stopping time of a hollow sphere filled with water and a hollow sphere filled with a more viscous fluid, such as honey or tar, is also brought up. While the Reynolds number does not directly apply in this situation, it is noted that viscosity is the relevant fluid property. The conversation ends with the poster seeking guidance and hints on this topic.
  • #1
noeszone
2
0
Hello! First time poster, long time lurker.

I've been doing my own independent study of fluid dynamics (not recommended, i know!) and I've hit a wall. I'm trying to imagine problems of fluid dynamics other than the "river and pipe" variety to confirm that I'm really getting this drag stuff. I'm curious to know if and how the Reynolds number Re can be adapted or defined in a way to describe drag in scenarios where a fluid is encased in a solid container that's moving around? Since its essentially about contact between a solid and a fluid, I should think it could be adapted to scenarios other than pipes, etc.

I'm curious to know because ... well, here's the problem I came up with in my head that I can't figure out:

Consider the following: Two hollow metal spheres are placed at the top of a hill. They are identical in every way (total mass etc), except for one: one is filled with water, the other is filled with something very viscous such as honey or tar. They are then released from the top of the hill and roll down.

Question: Do the spheres stop rolling at the same time, or does the honey sphere stop rolling first?

My "physics intuition" tells me that the honey sphere should stop rolling first, but I can't explain why in terms of drag, Reynolds or anything. I expect the honey sphere should stop rolling first because of higher viscosity, which would facilitate transfer of gravitational potential energy to thermal energy(heat transfer) as the sphere gains kinetic energy.

For that matter, what kind of fluid flow (if any at all) should one expect inside a hollow sphere filled with water that's spinning around or rolling? I can't even VISUALIZE it and I know from gen physics that's a bad sign :) All I can see is the fluid inside "lagging" behind the solid shell part of the sphere as it rolls, and then catches up due to fluidic drag... after it catches up, is the hollow sphere with fluid filled inside essentially the same thing as a solid sphere of same mass/density? (are there any random eddies inside that bring the fluid sphere to a stop sooner?)

ANY corrections or guidance or HINTS on this is appreciated. I've been through the definitions many times so I'm not sure reiteration will help at this point... but ill do that if y'all gurus think I should :)

thanks for reading. happy holidays )
 
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  • #2
You are correct that viscosity is the relevant fluid property, but the Reynolds number does not really apply here.

Modeling your problem is not trivial- you are setting up a time-dependent, spatially-dependent flow geometry, but some information can be extracted in limiting cases: very low viscosity as compared to very high viscosity, for example.

http://books.google.com/books?id=gtqjx_wuuDMC&pg=PA175&lpg=PA175&dq=%22fluid+filled+sphere%22+greenspan&source=bl&ots=BLc8pVfzIZ&sig=HrO2QupTPysO5XEUYImRzLhDFxk&hl=en&ei=-ivxTIzZJcignAfJieGeCg&sa=X&oi=book_result&ct=result&resnum=1&sqi=2&ved=0CBcQ6AEwAA#v=onepage&q&f=false [Broken]

http://www.google.com/url?sa=t&sour...sg=AFQjCNEb7HDAKdouhHbtmDnPbTX3d3b9cw&cad=rja

http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=382456
 
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1. What is the Reynolds number and how is it calculated?

The Reynolds number is a dimensionless number used to characterize the type of flow (laminar or turbulent) of a fluid over a surface. It is calculated by multiplying the fluid density by the flow velocity, the length of the surface, and dividing it by the fluid's viscosity.

2. How does the Reynolds number affect fluid drag?

The Reynolds number is directly related to the type of flow, and therefore, it affects the amount of fluid drag experienced by an object. At low Reynolds numbers, the flow is typically laminar and the drag is proportional to the viscosity of the fluid. At high Reynolds numbers, the flow becomes turbulent and the drag is proportional to the square of the flow velocity.

3. Can the Reynolds number be used to predict the behavior of a fluid?

Yes, the Reynolds number can be used to predict the type of flow (laminar or turbulent) and the amount of fluid drag experienced by an object. This is important in understanding how fluids behave in different situations, such as in pipes, around objects, or in airfoils.

4. How is the Reynolds number used in engineering and design?

The Reynolds number is an important factor in engineering and design, particularly in the fields of fluid dynamics and aerodynamics. It is used to determine the appropriate size and shape of objects to reduce fluid drag and improve performance. It is also used to determine the best type of flow (laminar or turbulent) for different applications.

5. Can the Reynolds number be manipulated to reduce fluid drag?

Yes, the Reynolds number can be manipulated by changing the properties of the fluid, such as its density or viscosity, or by adjusting the flow velocity or the size and shape of the object. By understanding the relationship between the Reynolds number and fluid drag, engineers and scientists can design more efficient and streamlined objects to reduce drag and improve performance.

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