Bernoulli seen from the molecular level

[hollus]

We often see Bernoulli based explanations about downforce creation. A typical example is the accelerated flow under the floor.

I'll avoid formulas beyond this one, courtesy of X:
Bernoulli says that total pressure is constant: Static pressure + Dynamic pressure, the latter as density * speed^2 / 2.

As a chemist, I learnt to think in terms of little things with mass, inertia, etc, interactuating with each other, be it single molecules or very small masses of air. I can see, understand and follow many aspects of downforce generation this way. My brain refuses to think in Bernoulli terms and I struggled for a good long time to understand it.

Marekk, in this forum, opened my eyes to how the description from the very small (individual gas molecules) and from the very big (Bernoulli) actually say the same thing in different languages. Now I think of Bernoulli as a way of expressing the conservation of energy, which manifests as pressure differences.

I am not saying that Bernoulli is wrong. It works, it has a solid scientific base, it predicts and explain things. I am just saying that there is another way of explaining the same phenomena from a different point of view.

I know that most people in this forum get confused by following molecules or very small masses of air, and feel more comfortable with the Bernoulli description of the phenomena. Just for the heck of sharing my point of view, I'll try to explain how the two relate to each other.

An ideal gas description of air works very well for this purpose, but it is important to remember that molecules of air are moving very fast, crashing on each other millions of times every second and hence constantly exchanging (kinetic) energy with each other. What we see from the outside are cumulative effects of many individual exchanges of energy between pairs of molecules, and those exchanges occur on a very fast timescale.
To get in the appropriate state of mind, imagine a concert in a really packed stadium, where everyone is touching the people around and jumping to the music, jumping which has a small and random horizontal component. Try to imagine what follows if suddenly 1000 people try to go to the same toilet at the same time.

Back to molecules, let's start with stationary gas. Imagine this between the car's floor and tarmac to give it some context. The blue circles are molecules. Think of the red arrows as velocity components (maybe at different times), that will later in time turn into forces.







Now let's assume that the same mass of air is moving. The concert analogy with going to the toilet works well here, we go from people jumping around at random to the music to people moving in a preferential direction.





And remember that air molecules are constantly exchanging energy with each other:






It is a bit confusing, it is difficult to see where energy is coming from and going to, but that is, simplified, how I see it. I hope it helps someone to get a different point of view on things. A useful mental exercise to help visualize these things:
Imagine that initial stationary mass of air between two equal masses of air, one to the left and one to the right of it. Now remove the mass of air to the right, put a perfect vacuum in there. What happens next?

[olefud]

I’m having trouble following; “Moving gas. Total energy is still constant”.

The static random energy I view as temperature. Taking movement as relative, it would seem that moving a wing through the static air would cause an acceleration of the static air, i.e. adding energy. After the wing passes and the air settles again, it should be warmer. Or not?

[hollus]

Yes, passing a wing through a static mass of air would leave energy there, and as you say, it will be (negligibly) warmer when it becomes stationary again.
When you start adding external objects and external energy, it is more difficult to see anything, as that external energy is likely to be blamed for everything that happens.

I can think of two situations where no external energy is directly being applied, yet the mass of air accelerates. One, from static to moving, would be when there is a low pressure area sucking the air in. It is difficult to argue for a sucking force (lack of pushing, really) to add energy to your system. In that case, the energy that sets the air in motion comes from inside the air mass itself, it moves when its movement stops being resisted.
Another scenario is air traveling through a wide pipe at constant speed. This is not a stopped/moving situation, but a slow/fast situation. The pipe then becomes narrower, then wider again. The air has to accelerate to pass through the narrow section to maintain mass flow, but air either side of it is at the same speed and pressure, so again, difficult to argue for anything adding energy there, and the energy spent in accelerating comes from inside (and gets recovered afterwards when slowing again). This is the usual Bernoulli system.

To be honest, unless one simplifies the system to the extreme it is quite difficult to follow. I am myself not 100% sure that all this makes sense. I assume it does because if fits perfectly well with what thermodynamics says, with what the molecular theory of gasses says when treated as statistical thermodynamics, and with what Bernoulli says.
http://en.wikipedia.org/wiki/Statistical_mechanics
It has been many years since I studied this and I am no longer fluent with all the formulas, I am just trying to apply the philosophic part.

[ankitshah]

This may seem pedantic but the explanation you gave does not account for the Bernoulli's principle. One important aspect of the Bernoulli's equations is that the temperature and the density of the fluid must remain the same.

In your explanation when the loss of energy as translation motion reduces the random component of the velocity the temperature observed reduces and hence not compatible exactly with Bernoulli. However if we consider the compressible nature of air and use the ideal gas theory we get results which are similar to the description you gave above meaning that when air is accelerated:
1) temperature, pressure, and density drop
2) the energy that manifested as temperature now is the energy of linear motion

[olefud]

Yeah, it’s been a long time for me too. I tend to operate qualitative rather than quantitative now. I suspect that your example is somewhat simplified to assume it’s entropy-free. And my hang-up is with the missing entropy.