# Fluid flow through square or rectangular passageways.

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Fluid flow is disrupted in the corners of square/rectangular passageways. The fluid tends to tumble in the corners. Can anyone tell me the name of this effect?

Turbulence

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Fluid flow is disrupted in the corners of square/rectangular passageways. The fluid tends to tumble in the corners. Can anyone tell me the name of this effect?

It has no specific name that I can think of, perhaps because it isn't the case.

Under normal 'no slip' conditions the fluid is stationary at the walls, and particularly so in the very corners. Moving away from the walls (and corners), the bulk fluid 'sees' less and less of any wall effect and ceases to have much interest at all in the shape of duct section. There is nothing to disturb the streamlines any more than any other standard section.

Change direction in a smooth curve and still no problems.

Turn a sharp right angle (is this what you were thinking of?) and now you're asking for infinite angular acceleration on the inside turn and downstream eddies will form. But this is true of all duct sections including circular

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I drove fire engines so I should remember this stuff. I do not. Getting old. Non laminar flow? I think there may be a formula expressing this. The larger the pipe the less the effect. An example: large water pipes or water mains, when they reach a critical large diameter create a mind of their own and flow high rates fairly independent upon the size and pressure. Smaller pipes tend to be more non laminar. More turbulent. Ratio of surface area to volume?

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Whether you have laminar or turbulent flow depends on the Reynolds number, which depends on velocity, viscosity and density of the fluid and "characteristic dimension". The last is tricky to determine in a bend.

I think "flow separation" is the term you might be looking for, where the nice laminar flow breaks loose from the surface and vortices are created. It is the same phenomenon that causes stall in airplane wings or wind turbines.

Now if this is for some reason critical, you simply don't use a straight corner, but a large radius curve.

Detailed paper with numerical simulations.

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Turn a sharp right angle (is this what you were thinking of?) and now you're asking for infinite angular acceleration on the inside turn and downstream eddies will form. But this is true of all duct sections including circular

Only mathematically not visually. The basic definition of laminar flow notes no mixing or churning which is quite different from described by the OP.

Whether you have laminar or turbulent flow depends on the Reynolds number, which depends on velocity, viscosity and density of the fluid and "characteristic dimension".

Why introduce additional factors? This seems to be a simplistic case based on one visual cue. If we are to select from laminar, turbulent or even transition region then turbulent seems to be the best choice. This is the situation I thought the OP described.

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Only mathematically not visually. The basic definition of laminar flow notes no mixing or churning which is quite different from described by the OP.

I recall neither the OP nor myself mentioning laminar flow.

'Churn flow' has a very specific understanding in fluid mechanics, which is not relevant here, If you intended 'formation of vortices' then you are incorrect: vortices can and must occur in general regimes of laminar flow to account for conservation of angular momentum. 'Mixing' also occurs in laminar flow whether by means of convection or molecular diffusion.

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Fluid flow is disrupted in the corners of square/rectangular passageways. The fluid tends to tumble in the corners. Can anyone tell me the name of this effect?

Personally I read this to mean transverse to the flow. That is to say flow in ducts of rectangular section. Bends, restrictions etc were not mentioned. Perhaps I was wrong but it certainly wasn't clear.

However since Larry has not returned to this site since he wrote the OP I wonder if he has lost interest?

I would like to extend a welcome to Ned, whilst pointing out that streamlines should not end as shown in post#6.

I call the reverse flow circulating in the corners simply 'eddys'. Such flow is not turbulent since full streamlines can be drawn at all points.

Edited by studiot

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I recall neither the OP nor myself mentioning laminar flow.

The OP mentioned about fluid tumbling which is visual reference not based on a mathematical equation. For a visual reference there is generally three cases.

'Churn flow' has a very specific understanding in fluid mechanics, which is not relevant here

Then why did you mention it? I said said churn i.e. to mix up, swirl etc.

If you intended 'formation of vortices' then you are incorrect: vortices can and must occur in general regimes of laminar flow to account for conservation of angular momentum. 'Mixing' also occurs in laminar flow whether by means of convection or molecular diffusion.

I said eddies not vortices. Again not by the basic definition:

In fluid dynamics, laminar flow (or streamline flow) occurs when a fluid flows in parallel layers, with no disruption between the layers.[1] At low velocities, the fluid tends to flow without lateral mixing, and adjacent layers slide past one another like playing cards. There are no cross-currents perpendicular to the direction of flow, nor eddies or swirls of fluids.[2] In laminar flow, the motion of the particles of the fluid is very orderly with particles close to a solid surface moving in straight lines parallel to that surface

Personally I read this to mean transverse to the flow. That is to say flow in ducts of rectangular section. Bends, restrictions etc were not mentioned. Perhaps I was wrong but it certainly wasn't clear.

However since Larry has not returned to this site since he wrote the OP I wonder if he has lost interest?

I would like to extend a welcome to Ned, whilst pointing out that streamlines should not end as shown in post#6.

I call the reverse flow circulating in the corners simply 'eddys'. Such flow is not turbulent since full streamlines can be drawn at all points.

Thanks for the welcome. I found a slightly different photo that gives the same basic explanation.

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The OP mentioned about fluid tumbling which is visual reference not based on a mathematical equation. For a visual reference there is generally three cases.

Then why did you mention it? I said said churn i.e. to mix up, swirl etc.

I said eddies not vortices. Again not by the basic definition:

Please don't quote Wikipedia at me. Most of the fluid flow entries seem to have been written by aeronautical engineers, and they tend to have very limited bandwidth in the field.

Edited by sethoflagos

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Please don't quote Wikipedia at me. Most of the fluid flow entries seem to have been written by aeronautical engineers, and they tend to have very limited bandwidth in the field.

Fair enough.You're entitled to label any collective group as having a 'very limited bandwidth' on a subject. I wholly disagree with your generalized statement shown above. If an aeronautical engineer sees your comment perhaps they'll share their thoughts. Until then let's see what Dr. Colin Caprani (Ceng.) "Fluid Mechanics 2nd Year Civil and Structural Engineering" notes about the characteristics of laminar flow:

For laminar flow: ‘low’ velocity; • Dye does not mix with water; • Fluid particles move in straight lines

http://www.colincaprani.com/files/notes/Fluid%20Mechanics.pdf

That seems very similar to the earlier definition. Surely, you don't disagree with the distinguished author?

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That seems very similar to the earlier definition. Surely, you don't disagree with the distinguished author?

Strangely enough.....He's presenting a simplistic model for students in a discipline that rarely need worry itself with the full picture.

I guess by 'particles' he means what we usually describe as 'fluid parcels' in the literature, and, yes, in pure laminar flow, fluid parcels are constrained to simple streamlines, and eddy diffusivity is zero.

But you cannot extend this reasoning down to the molecular scale because individual fluid molecules move in anything but a straight line. So at the boundaries of fluid parcels and streamlines there is constant material (and momentum, and thermal) flux across those boundaries. If there is a higher concentration of dye in one streamline, there may be no convective mixing, but there is definitely nett movement of dye in the direction of negative concentration gradient into adjacent streamlines of lower dye concentration through the mechanism of molecular diffusion.

To paraphrase an ancient and not particularly good engineering joke, one may in certain instances quite reasonably commence an analysis with the phrase 'assume spherical chicken'. Even if this analysis proceeded to provide an excellent fit with experimental data, it would take a particular kind of fool to conclude from this that all chickens were indeed spherical.

Beware simplifying assumptions. They are only useful approximations; they are not fact.

Edited by sethoflagos

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I thought aeronautical engineers used spherical chickens to test the robustness of jet engines.

One should also beware the subtle and not so subtle differences in terminology used by different authors at different times.

Streamlines constitute a direction field and must either extend to infinity or form closed loops.

Either way if you can draw streamlines it is possible to predict where the flow will go next from any point.

That is not turbulence, where it is impossible to predict the next destination from any particular point.

Remember also that there are two kinds of vortex, one with net vorticity and one without.

The vortex sheets shown in the Wikipedia article are actually a result of Kelvin's theorem and the above statements.

They are the loop closers required by Kelvin to generate the vorticity (circulation) to generate the lift.

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I thought aeronautical engineers used spherical chickens to test the robustness of jet engines.

Nothing against aeronautics engineers btw. It's simply that flow of air around various solid body sections within very restricted ranges of pressure and temperature corresponds to an extremely narrow band of interest within the vast, rich universe of Navier-Stokes.

Is it more efficient to stir coffee with a teaspoon or a fork? Strangely, I've found Wikipedia unusually silent on this commonplace, everyday dilemma.

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Strangely enough.....He's presenting a simplistic model for students in a discipline that rarely need worry itself with the full picture.

Beware simplifying assumptions. They are only useful approximations; they are not fact.

OP asked a simplistic question; I gave a simplistic answer. Overcomplicating can be problematic.

Streamlines constitute a direction field and must either extend to infinity or form closed loops.

I don't think those are streamlines but rather a limited version called flow path.

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I don't think those are streamlines but rather a limited version called flow path.

studiot's usage of the 'streamline' terminology is absolutely correct.

Any other related term (pathline, streakline, timeline) would not be consistent with his explanation of it's relationship to the instantaneous flow velocity vector field.

Perhaps you should be asking questions rather than trying to rubbish other people's answers........?

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studiot's usage of the 'streamline' terminology is absolutely correct.

Any other related term (pathline, streakline, timeline) would not be consistent with his explanation of it's relationship to the instantaneous flow velocity vector field.

Perhaps you should be asking questions rather than trying to rubbish other people's answers........?

Explain the inconsistencies stated by studiot, why do the noted 'streamlines' behave unlike typical streamlines? Explain how book's fact checkers could make such a big error in something so basic? Explain the odds that another source would make the same mistake? http://images.slideplayer.com/39/10965492/slides/slide_23.jpg

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Explain the inconsistencies stated by studiot, why do the noted 'streamlines' behave unlike typical streamlines? Explain how book's fact checkers could make such a big error in something so basic? Explain the odds that another source would make the same mistake? http://images.slideplayer.com/39/10965492/slides/slide_23.jpg

This clip seems to get across the key ideas quite clearly.

What catches most people out is the deep contrast between steady state flow and unsteady (or dynamic) flow. This is not synonymous with laminar vs turbulent.

Laminar flow can be dynamic without being turbulent. And despite laminar often being described as streamline flow, streamlines exist in turbulent flow too. Other than maybe some extreme situations such as a shock wave front, there is always an instantaneous velocity vector field with no discontinuities between the vectors (thanks to the continuity equation), so streamlines can be drawn.

Edited by sethoflagos

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I have already noted that we do not know if Larry Hills was referring to the cross sectional or longitudinal flow pattern, and that I assumed the more difficult cross sectional question.

Rectangular/square cross sections are usually used for gaseous flow rather than for liquids for a number of reasons.

Further this flow is often turbulent rather than laminar, at least in the longitudinal direction.

I note the presentation quoted in post#17 is an elementary presentation, slanted towards liquids (water in particular) in round sectioned pipes.

In the quote below, from the Karlsruher Institute I have highlighted the classic 8 vortex pattern for square ducts and,

As the professor says cross sectional profiles are less abundant than longitudinal ones.

The patterns of eddies are known as disturbed flow.

It is also called secondary flow in that it is distinct from the main flow of the bulk fluid.

If you would like me to explain the various flow terminology I will happily oblige.

But it is important to distinguish between pathlines, which have one more dimension than streamlines, streaklines and streamlines themselves.

Further important terms are steady/unsteady and uniform/nonuniform flow, turbulent, laminar and disturbed flow and to know which is the 'opposite' of which.

Edit there is one other important flow distinction viz compressible v incompressible, obviously important in water v gas as the fluid.

Fluid flow in a straight duct with rectangular cross-section exhibits turbulence-induced secondary motion of small amplitude, but with a large effect on momentum, heat and mass transport. As an example, the wall shear-stress varies strongly along the wall-bounded perimeter, with possible consequences for sediment erosion. The mean secondary flow in a square duct bounded by four solid walls has the well-known 8-vortex pattern. At relatively low Reynolds number, the formation of the large-scale average vortices in the cross-section is due to statistically preferred locations of near-wall coherent structures in the vicinity of the corners [1,2]. The scaling with Reynolds number of this phenomenon is currently still an open question. When the duct cross-section has an aspect ratio other than unity and/or one of the boundaries is not a solid wall (e.g. a free surface), the shape of the pattern is even less well documented.
Edited by studiot

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I have already noted that we do not know if Larry Hills was referring to the cross sectional or longitudinal flow pattern, and that I assumed the more difficult cross sectional question.

.........

In the quote below, from the Karlsruher Institute I have highlighted the classic 8 vortex pattern for square ducts and,

As the professor says cross sectional profiles are less abundant than longitudinal ones.

Aha!

I wish you'd yelled 'Prandtl!' at me after post #2 ;-)

This must be the effect the OP has seen. But the question is where? Years of weekly air flow measurements inside paper machine drying hoods; working with gas ducting up to 27 feet square section; and not to mention countless ciggies smoked in draughty passageways; and the effect has always been swamped by bulk flow.

Edited by sethoflagos

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I drove fire engines so I should remember this stuff. I do not. Getting old. Non laminar flow? I think there may be a formula expressing this. The larger the pipe the less the effect. An example: large water pipes or water mains, when they reach a critical large diameter create a mind of their own and flow high rates fairly independent upon the size and pressure. Smaller pipes tend to be more non laminar. More turbulent. Ratio of surface area to volume?

Rather than the larger the cross section it is the closer the flow rate is to the maximum capacity of the total volume including the frictional loses in the turns of the pipe. Square pipes tend to have maximum flow rates near the center as they reach the maximum flow rates. This usually is a round. In rectangular pipes it is more ovular. But turns especially near the entrance and exit have more effect than near the center of the length.

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