Bernoulli and direct-air jet when using overhead vents

There is this famous experiment to demonstrate the Bernoulli effect, where you try to very rapidly inflate a loose air balloon of sorts, like shown for example in this video. Here's a still image so you know what I'm talking about:

The point being that if you have a fast air stream from a nozzle (like your mouth), it will pull a lot more air with it compared to just the air in the stream itself. Fine. That's just Bernoulli at work.

Now, let's travel (preferably somewhere nice ;) ), and in buses or airplanes you have seen these vents in the ceiling above your seat:

Let's assume that the air coming from the vent is perfectly clean (an excellent approximation, at least in airplanes given their filtration systems), whereas there is some contamination in the surrounding air. Most relevantly, that could be viruses and bacteria, or more easily to experiment with, imagine some odor (and I'm sure you have an easy time imagining that...).

Now, my experience (with the latter scenario) seems to indicate that opening the air vent fully indeed does more quickly reduce the unwanted pollutants to low levels. However, it is not clear to me why that needs to be the case, given the Bernoulli effect, and I lack a solid intuition. Thus my question:

Given the Bernoulli effect, how do ceiling vents in airplanes and buses help to quickly reduce unwanted contaminants in the air? Are there limiting cases in which either the direct air stream dominates, or the air pulled in via Bernoulli, or the overall turbulence caused by the air stream?

Edit: to clarify, is there a general way to estimate the amount of air that comes directly from the air vent, versus the amount of air that is additionally pulled in through the Bernoulli effect?

• Bernoulli's principle no longer applies when you've added energy with a jet. Feb 8, 2023 at 13:20
• @D.Halsey not sure I understand. Clearly the demo in the linked video works based on the Bernoulli effect. "Jet" here just means a stream of air coming out of a nozzle. Am I misunderstanding your comment?
– rfl
Feb 8, 2023 at 13:44
• Cf. the video maker's web site, pbsdll.k12.sd.us/Downloads/7/21418/Bernoulli2019b.pdf (see page 6). This seems to be designed for use on pupils at school and not university-level teaching. (Obviously, at school an explanation will most likely not involve entrainment or an anisotropic stress tensor...) Mar 22, 2023 at 6:34
• For your edit: As I already tried to hint at, the key-word you need to be researching is "entrainment". Try this, for example: doi.org/10.1017/S0022112086001222 Depending on how deep you want to dive into this. Or try introductory books on meteorology, e.g. R.S. Scorer: Environmental Aerodynamics (he actually references the Bernoulli effect in this context and calls the explanation using it "misleading" (Chapter 2-11, p.76)). Mar 27, 2023 at 15:19
• thanks @kricheli, that's useful... note the extra bounty that needs to be distributed to somebody writing an answer ;)
– rfl
Mar 27, 2023 at 15:35

Aircraft cabins are designed to completely replace the air every 2-3 minutes. The air vents help do this by introducing clean, filtered air, and by creating a continuous flow of air, as pictured.

(Image source here)

Intuitively I see your concern about the vents mixing the air you breath with those around you (and you do see a bit of this if you look at some of the airflow simulations linked in the above website, like this one). But consider the opposite limit, in which the air is completely stagnant (no air currents or convection). In this case, any odor sources near you will diffuse outward from the source, so you'll still breath it in. And because the air isn't being replaced, the concentration of odor molecules/virus particles/whatever will keep increasing. This is why people made a big deal during the height of the Covid 19 pandemic about opening a window if you were going to spend time indoors with someone.

Update - comparison away from limiting cases

As noted in the comments, a comparison with the stagnant air limit isn't r really fair, as there's still plenty of air circulation even when you turn off your own personal air vent.

We can maybe think about the following 3 effects of turning on your own vent:

1. The increase in the rate at which dirty air around you is displaced by the additional fresh air
2. The change in the pattern of large-scale air currents
3. The local drawing in of surrounding air due to vortices formed at the boundary of the air jet (see answer by kricheli)

Quantitatively understanding all of this is very complicated, and I don't think it's possible to give a confident answer without doing proper finite-element simulations. But I suppose there are a few potential observations worth noting anyway:

• Going back to the original demo video that you linked, it's true that the majority of the air that you feel from the vent is actually air drawn in from the surroundings, rather than from the jet itself (so 1 is less significant than 2 and 3). But that air is still coming from above your neighbors' heads (unless they're a lot taller than you, I suppose). And so (presumably) most of that air is actually sourced by more powerful vents than the ones they let you control (which are at the top of the cabin above the isle in the above picture).
• Again because the vent directly above your head is relatively weak, it probably doesn't have such a huge effect on the overall airflow in the cabin. But if anything, it should pull air from your neighbors downward, removing particulates in the process.

But this is all speculation. I did come across a few more simulations on YouTube here. Maybe you can imagine how things would change if an overhead vent was turned on. Or better yet, bring a few bits of string on your next flight and try to visualize how the air currents change for yourself! (though preferably only if you're sitting next to someone you know).

• I appreciate your suggestion to go to the extreme case of completely stagnant air, and in that situation your answer is certainly correct. However, that's not quite the situation in reality, is it. I at least find it quite conceivable that by opening an air vent, the extra air pulled in might INCREASE the local concentration with contaminants by more than what otherwise would only be increased through diffusion. That's the situation where I lack intuition to justify why opening the jet has to reduce the contaminants locally.
– rfl
Mar 27, 2023 at 14:42
• I updated the answer to address this. It's subtle. Maybe Feynman could think of a simple, convincing argument one way or the other, but I can't be sure what the net effect would be. Mar 29, 2023 at 1:09
• Thank you for a nice answer. I wish we could split the bounty :)
– rfl
Mar 29, 2023 at 12:48

Ok, to expand on my comment above:

A nice source for this might be the book "Evinronmental Aerodynamics" by R.S. Scorer, Ellis Horwood Ltd., Chichester, 1978. Much of my explanation is taken from it. But other introductory books on meteorology and/or turbulence might suit you as well.

What happens in the experiment with the Bernoulli tubes is that exhaling, i.e. releasing a continuous stream of air from high pressure (in your mouth) into the air surrounding your head, will create a turbulent jet. The boundary layer between the fast-moving stream exiting the nozzle (your mouth) and the surrounding air has an instability, vortices form and air is drawn into the jet. Because of the turbulence involved the Bernoulli equation is not applicable and the explanation given in the video is oversimplified/wrong.

A nice remark by Scorer on this (p. 77):

If flow were reversible it would be most inconvenient for animals, because unless they were moving or there was a wind they would breathe in at each breath the air breathed out from the last one. [...]

And then, further:

I a jet the momentum flux is the same at all distances along it, therefore $$R^2 W^2$$ is constant, the cross section area being represented by $$R^2$$, and the axial component of velocity $$W$$ being proportional to the volume flux and also to the 'density of momentum'. If $$W$$ is to decrease then $$R$$ must increase in proportion, and so the volume flux, which is proportional to $$R^2 W$$, increases. This means that the jet can only slow down by carrying a greater volume with it, which means that there must be entrainment, and this is initiated by the instability of the vortex sheet. The low pressure is not produced by the high velocity in the jet but only by its mixing with the ambient fluid. Thus a water jet can cause low pressure by entraining air, a fact made use of in the vacuum pump attached to the tap in the chemistry laboratory.

In chapter 8.9 he gives an analysis to show that in a certain regime (sufficiently far away from the orifice) the radius $$R$$ of the jet grows proportional to the distance $$z$$ travelled from the nozzle. (Including nice illustrations btw., you may find something similar when searching for "turbulent jet" on the internet.)

This might be a good starting point for you, or you have a look at something like https://doi.org/10.1017/S0022112086001222.

You might also want to read a little bit (just the qualitative idea perhaps?) about turbulent diffusion - in short: turbulent airflow lets pollutants (like the molecules your seatmate expelled when sneezing or farting) diffuse much more swiftly than molecular diffusion does.

For the concrete application to airplane cabins I can't give you much info. A good question would be how important turbulence is in this in comparison to the role of air filters. Cf. the answer by user34722.