# Is my understanding of density/speed correct?

So I asked this question, and I wanted to know if my guess below was correct. I got an answer in the comments, but the reason for asking this question is because I was still a bit confused if my thinking was correct, if that makes sense. (the below is copy/pasted from the linked question) Also, if this question is considered a duplicate or goes against any guidelines, I'll happily delete it. (I did read this page, on what questions to ask and what to avoid.)

My guess of what happens with density at higher and lower speeds is the following (my guess is that it's a non-linear relationship) : The air density doesn't change much until you reach Mach ~0.3, where Bernoulli's equation isn't valid anymore, so the density can't change but so much, or Bernoulli's equation would be false, even below Mach 0.3.

When you go faster, there are less air molecules to 'bounce' off of the surrounding body and each other (because at high speed, the surrounding air is less dense), so changing speed doesn't do as much as it would at a lower speed, if that makes sense. (I might be wrong about some of those statements.)

I think if I explain my guess of why density doesn't change much up until Mach 0.3, it might clarify things. So if you have normal-density air (like still air at room temp) and you start to speed it up, a few things happen.

The air molecules bounce off of each other less, because they all have a forward speed component now, and they 'bounce' less on the surrounding container/body, both creating a lower density air. Doing this at lower speeds, there are more molecules, and because there are so many, speeding up doesn't prevent the 'bouncing' as much as it does at higher speeds. (Again, I might be wrong about some of those statements.)

• Going back to basics may help here. If air molecules "bounce off each other less", the air is cooler. Pressure is a function of Density and Temperature. I would not conflate this with Trans-sonic "Gedanken experiments" for now. Commented Jan 16 at 10:02
• @RobertDiGiovanni ah okay I see. So I’m kind of confused about how the Gedankin experiment answer ‘works’ because you made a good point about pressure vs. temperature. Commented Jan 16 at 16:34
• I know it can be confusing because, even in a wind tunnel, "wind flow" is not entirely accurately portrayed (but good enough to get some solid research done). In reality it's the air reacting with the wing in motion. This is why they say air isn't compressed (at lower Mach), it just gets moved out of the way. The Gedanken experiment seemed to deal with pressure differences behind the shockwave at transonic speeds. This took a lot of years for many people to figure out. Commented Jan 16 at 18:35
• @RobertDiGiovanni hmm okay. I came across this answer, and if you look at the bottom of it, you'll see a part about density. Could you explain what it means, because it says "A speed increase is always coupled to a decrease in density." which is confusing because at this point I'm not sure if density increases or decreases with speed. Thanks Commented Jan 16 at 18:52
• density where? I believe they are talking about phenomena behind the shockwave. But is density vs velocity a function of air itself? Or is it (as pressure, Bernoulli) that a moving air (or water) stream draws air away from a surface, creating lower pressure, ergo density? Air simply moves from high pressure to low. To have a significant change in density (along the path of the airstream, within a few meters) would require one heck of a pressure differential. Commented Jan 16 at 21:19