Demystifying the Often Misunderstood Bernoulli's Equation - Comments

[boneh3ad]

Greg Bernhardt submitted a new blog post

Demystifying the Often Misunderstood Bernoulli's Equation

Continue reading the Original Blog Post.

 

[kuruman]

It is mentioned in the text that "Given that the fluid velocity is everywhere normal to the streamline, no flow can cross such lines." Surely that's a typo. The accompanying drawing correctly shows the local velocity vectors tangent to the streamlines.

 

[boneh3ad]

It is mentioned in the text that "Given that the fluid velocity is everywhere normal to the streamline, no flow can cross such lines." Surely that's a typo. The accompanying drawing correctly shows the local velocity vectors tangent to the streamlines.

Good catch.

Let's just say I am averaging about 4.5 hours of sleep over the past 3 weeks but thought this article addressed a misconception that is so frequent that I thought it worthwhile to attempt to write it now anyway. If anyone finds other blatant typos, please let me know.

 

[kuruman]

4.5 hours of sleep over the past 3 weeks

Wow! This is$$\frac{4.5~hr}{the~past~3~wk}=1.5\frac{hr}{the~past~wk}.$$You oughta get more sleep than that.

 

[boneh3ad]

Wow! This is$$\frac{4.5~hr}{the~past~3~wk}=1.5\frac{hr}{the~past~wk}.$$You oughta get more sleep than that.

Now you are catching me in more poorly-worded statements that may or may not be related to sleep deprivation.

 

[Swamp Thing]

Hi,

Congratulations! There has long been a need to demystify Bernoulli's principle, and this article surely fills a significant part of that vacuum.

Having said that, I'm not sure what fraction of the target audience (meaning people who actually need to be demystified) would be able to take profit from this particular level of exposition. I'm not an expert (which perhaps entitles me to represent the mystified ones). Is it the case that people with enough math and physics competence to understand the article are in fact likely to have held wrong ideas before reading it? For example, believing in some of the wrong notions of aircraft flight that we often find on YouTube etc? And when I say wrong notions, I mean that other people, the debunkers, say that they are wrong -- and not that I'm personally qualified to point out the errors in precise terms.

What I'd like to suggest is, maybe you could write a companion article that (a) makes the principle come alive using more intuition (graphics) and less calculus and (b) debunks specific misunderstandings that people have about airplane wings, balls floating in jets and so on. To sum up, something to address misconceptions among laymen, as much as misconceptions among specialists.

Of course, it may turn out that it is impossible to do justice at all to these things without the kind of mathematical support that you have already used in the article. I don't know.

Thanks!Edit: There's a lot of stuff out there that tries to straighten out the subtle business of Coanda Effect versus Bernoulli effect, but personally I'm still not clear about this kind of thing. This could be one thing that you could perhaps clarify, should you decide to go ahead with the companion article idea.

 

[russ_watters]

Having said that, I'm not sure what fraction of the target audience (meaning people who actually need to be demystified) would be able to take profit from this particular level of exposition. I'm not an expert (which perhaps entitles me to represent the mystified ones). Is it the case that people with enough math and physics competence to understand the article are in fact likely to have held wrong ideas before reading it? For example, believing in some of the wrong notions of aircraft flight that we often find on YouTube etc? And when I say wrong notions, I mean that other people, the debunkers, say that they are wrong -- and not that I'm personally qualified to point out the errors in precise terms.

What I'd like to suggest is, maybe you could write a companion article that (a) makes the principle come alive using more intuition (graphics) and less calculus and (b) debunks specific misunderstandings that people have about airplane wings, balls floating in jets and so on. To sum up, something to address misconceptions among laymen, as much as misconceptions among specialists.

It's a difficult balance between being concise and being complete. A "concise" answer is likely to have holes or thin spots that create an opportunity to be or be perceived as wrong or, well, incomplete, whereas a "complete" answer may lose part of the target audience who is looking for a fast answer to a small question.

The title and intro look a bit like a hook to bring people in for a quick answer to a particular misconception or two, but really is a pretty complete explanation...frankly, a quick list of two or three misconceptions would be too short for an article. But I'll provide a concise example of what I think is the most common misconception we get about Bernoulli's principle itself (not the applications such as lift):

Many people don't grasp the full implications of the steady flow and streamline assumptions. We often get people who ask, "but what if we add an orifice...?" or "what if I use a smaller pipe?" Now, not only is it no longer the same streamline or steady flow, but it isn't even the same system!

There's an active thread in biology right now where someone asks; shouldn't the volumetric flow rate through a small straw be the same as through a large straw because a lower cross sectional area results in higher velocity? We often get this very misconception with regard to blood circulation. As described, this is called "continuity" (not specifically mentioned in the insight), but it doesn't apply across two different systems. Continuity says that the mass flow rate in two parts of the same system must be the same unless mass is accumulating or draining. But of course the mass flow rate in two different systems doesn't need to be the same.

 

[boneh3ad]

A couple of things here:
First, I didn't create the title. I don't know who is in charge of that, but I submitted the article and it magically appeared with a title. I agree it does give off the air of being written at a lower level than it is.

Second, I did try to start it out by saying it was written for someone already familiar with some basic undergraduate-level math and science. There are a surprising number of people at this level with a lot of misconceptions. It's certainly not the majority of them, but a sizable chunk.

Third, I agree that, when this article was finished and I looked back over it, it turned out to be at a higher level than my original intention. This came from going back over it and filling in enough holes to try to make it "reasonably complete" but without digging into, for example, the derivation of the energy equation. I don't honestly see any way around this at this point if I do it from an energy approach, and there are myriad sources online who discuss the same issue from the point of view of a force balance (conservation of momentum).

Finally, I also agree that there is a need for a similar article (or maybe an expansion of this one is some way) that does address this at a lower level, but I am just not sure how to implement it without an appeal to authority rather than letting the math/physics speak for themselves.

(a) makes the principle come alive using more intuition (graphics) and less calculus

Part of the issue is that fluid dynamics is particularly counterintuitive for many people who don't have any training in the topic. I am not how to appeal to their intuition when it often serves them wrong in the first place. I was the same way when I was first learning and it all felt backward.

(b) debunks specific misunderstandings that people have about airplane wings,

https://www.physicsforums.com/insights/airplane-wing-work-primer-lift/

 

[Swamp Thing]

I guess fluid mechanics is a bit like quantum mechanics in being highly counter-intuitive, although for different reasons

Perhaps even more confusing than QM in some sense, given that there is a Clay Millennial bounty for the Navier-Stokes theorem but none for a QM problem.

 

[boneh3ad]

Heisenberg quit fluids to do QM. Draw your own conclusions.

 

[Swamp Thing]

So he decided to go for the low-hanging fruit...

 

[ruko]

Greg Bernhardt submitted a new blog post

Demystifying the Often Misunderstood Bernoulli's Equation
View attachment 235151Continue reading the Original Blog Post.

All those formulas. I don't have a Pizza hut Delivery to my name so they could be mean anything. What I really would like to know is the Bernoulli affect the main reason why airplanes can fly? If it is, then I wonder how airplanes are able to fly upside down.

 

[boneh3ad]

All those formulas. I don't have a Pizza hut Delivery to my name so they could be mean anything. What I really would like to know is the Bernoulli affect the main reason why airplanes can fly? If it is, then I wonder how airplanes are able to fly upside down.

Again, as linked before, there's a totally separate article for that.

https://www.physicsforums.com/insights/airplane-wing-work-primer-lift/

 

[Swamp Thing]

That lift article is just perfect for the (fairly) uninitiated.

Quick question. You said there:

Why does the air move faster over the top, and for that matter, how do we know how much downwash is produced?
It turns out, these two questions are related, and also why lift is incorrectly explained so often. It also turns out that the answer to this question is extraordinarily complicated. The simplest answer is that inviscid theory predicts one stagnation point at the front where the air impacts the tip of the airfoil, and one at the back at some arbitrary point that would result in no lift and no flow deflection.

A rough hand sketch of this non-viscid case would be nice. Or even better, the following simulation with viscosity set to zero -- how would that look?

 

[boneh3ad]

If that flow was inviscid, the flow on bottom would wrap around the sharp trailing edge and leave the shape somewhere back around on the top surface.

 

[Swamp Thing]

I just realized that the animation in your Lift article (i.e. the one I pasted in my previous post) is actually showing inviscid flow, not viscid flow. So that answers my question. I had wrongly assumed that this is viscid flow.

I guess it makes kind of sense, because the incoming and outgoing angles are nearly equal for each and every streamline, hence no net momentum change so no lift.

Edit: Wait, that's obviously not correct. The lines are asymptotically horizontal downstream, which is what matters.

It may be instructive to see the streamlines side by side for exactly the same airfoil, with and without viscosity.

 

[russ_watters]

What I really would like to know is the Bernoulli affect the main reason why airplanes can fly? If it is, then I wonder how airplanes are able to fly upside down.

It's complicated, so I wouldn't say it's the main effect, but it is always in effect. The simple answer to your question is that the strength of the effect depends on the angle the wing makes with the wind, and that angle is different for an inverted plane than an upright plane.

 

[cjl]

I just realized that the animation in your Lift article (i.e. the one I pasted in my previous post) is actually showing inviscid flow, not viscid flow. So that answers my question. I had wrongly assumed that this is viscid flow.

It's inviscid, but it's including an important element of viscous flow. Specifically, inviscid theory alone would predict streamlines more like the top image shown here (which would generate zero lift):

Viscosity is what enforces that the flow comes smoothly off the sharp trailing edge of the airfoil, modifying the flow from the top image to the bottom image. Frequently, when analyzing lift and flow about an airfoil, it is modeled as inviscid, but with this condition of smooth flow off the trailing edge enforced to give you a physically reasonable flow.

 

[Swamp Thing]

In figure (a), assume that the wing has negligible density compared with the fluid. It is constrained from rotating or moving left / right. But it is totally free to move up or down (no restoring force in Y direction).

In that case, would it drift downwards over time? And if we now add a constraint against this drift, how much force would we measure?

Edit:
MbahahahaHA! I believe I got it!
Let's assume the wing does have some mass (a lot, in fact). But since there is no viscosity, the liquid can't drag it along -- the wing just hovers there, provided that we have made sure to give it an initial push to the left during the setup phase when the liquid was accelerating. Newton's first law and all that?

In steady state, the wing bends the streamlines by virtue of just being there occupying space, rather than "pushing back" to the left.

Edit Edit: This would work nicely if the wing had the same density as the fluid. It would hover in place without needing any constraint, yet shape the flow as in Fig. (a).

 

[Swamp Thing]

I guess fluid mechanics is a bit like quantum mechanics in being highly counter-intuitive, although for different reasons

Perhaps even more confusing than QM in some sense, given that there is a Clay Millennial bounty for the Navier-Stokes theorem but none for a QM problem.

Wait, I was wrong there... there is a QM problem in the Clay Millennium list.. http://www.claymath.org/millennium-problems/yang–mills-and-mass-gap