## Speed limit of pressurised air

How fast can air go when under pressure? Is there a formula that describes this. I was just wondering how much faster air can go when put under more pressure. Also, what is the acceleration rate of the air?

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 That depends on many, many variables, from the relative pressure of the air and the ambient air outside, the temperature of the air, the shape of the duct it passes through, etc. There exist wind tunnels that accelerate compressed air to Mach 20, or 20 times the speed of sound, for example.
 Wow, that's pretty fast. Alright, 25 degrees Celsius, ambient air pressure of 15 psi and the shape of the duct can be an 8mm cylinder. And the pressurised air for a round number can be 100 psi. So what is done with these variables to find out the speed limit, and acceleration?

Mentor

## Speed limit of pressurised air

I think you have two different questions here.

 How fast can air go when under pressure?
There is no theoretical speed limit, just experimental issues.

How fast can air go when expanded from pressure 1 to pressure 2? This can be approximated with energy conservation: If you take a volume V of compressed air and expand it to V' uncompressed air, you gain energy, which can be used to accelerate the air. This is an adiabatic process, and I think you can find the relevant formulas here, at Wikipedia or whatever.

 As I am new to physics, those equations go way over my head... Is there a simple way to roughly estimate the speed of compressed air? (With force and length known) I was reading a similar post, and someone said something about a natural speed limit of air molecules, however I couldn't find any other references to this. Is this actually the case?
 There is no natural speed limit of air particles. With your simple pipe example you could get a really good approximation using Hagen-Poiseuille flow. For a more general case you could get a very rough approximation using the Bernoulli equation and a better estimate with correction factors such as the Darcy-Weisbach equation. It all just depends on your situation.
 Ok, I am looking for simple equation that will give a rough approximation (± 10m/s). I guess, through finding this, I want to be able to answer a question from one of my other topics, that remains unanswered - Speed of a projectile propelled by compressed air. The barrel length is 0.82m long with a diametre of 50.27cm2. The capacity of the air tank is 24L. The weight of the projectile is 4 grams. What other factors are needed in the equation to give an approximate answer? Any variables that will affect the answer only slightly (1m/s), I don't see as neccesary if the complicate it... Also, with no natural speed limit of air molecules, does this mean they will get faster and faster with more force behind it, with no limit except c?

Mentor
If you always accelerate the particles in one direction, they can get faster and faster (with c as limit of course).
However, compressed air will fail to do so, as soon as you are close to the speed of sound.

 Ok, I am looking for simple equation that will give a rough approximation (± 10m/s).
That should be possible by putting the equations together, and I am too lazy to do this (it is basic algebra).

With the projectile, you can use the projectile mass instead of the air mass, as the latter one will be negligible for reasonable setups.

 Tags acceleration, air, pressure, speed, speed limit