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Comment by AnotherGoodName | Hacker News Reader

I'm guessing that the speed of sound being different in the high pressure side vs low pressure side helps this occur.

When you think about it it's hard for air to push itself faster than the speed of sound since the speed of sound is literally the speed that a wave of compression in air will propagate.

So how can it go faster than the max speed a wave of compression can travel at when it's powered by that? Well compressed air has a much higher speed of sound. So it's accelerated to the below speed of sound inside the nozzle and on exit it's now faster than the speed of sound, not due to further acceleration beyond the speed of sound but due to the speed of sound suddenly dropping in the lower pressure.

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The speed of sound does not depend on pressure, only temperature.

I suspect this is occurring because the (sonic) flow through the nozzle cools as it expands, therefore the speed of sound drops, making the same flow now supersonic in the cooled gas.

This was interesting so I looked it up

>For a given ideal gas the molecular composition is fixed, and thus the speed of sound depends only on its temperature. At a constant temperature, the gas pressure has no effect on the speed of sound, since the density will increase, and since pressure and density (also proportional to pressure) have equal but opposite effects on the speed of sound, and the two contributions cancel out exactly.

https://en.m.wikipedia.org/wiki/Speed_of_sound#Dependence_on...

I never knew this either. This makes sense as when you tap on a propane tank they always sound empty, different than a metal tank of water. Even though it's a liquid and under extreme pressure, it's only the temperature that matters.

Liquid propane is definitely not an ideal gas.

Not saying it is, but it's very volatile. It really doesn't want to be a liquid at room temperature. I can't tell if it's empty or full when a tap on it, but definitely can with with water. It's an impedance thing.

I'm just saying a fact about ideal gases doesn't really imply anything about LP.

It does, vapor pressure.

That's got nothing to do with some fluid behaving like an ideal gas or not. Also, except for very low pressures, vapor does not behave like an ideal gas.

Sure it does, it's riding the border of a phase change between gas and liquid. It's in a super compressed equilibrium so it's going to behave similarly to an ideal gas.

That's - not how that works. I suggest you look at any fluid data `riding' that border. "Super compressed" and "ideal gas" are mutually exclusive. "Equilibrium" has even less to do with any of that.

That's because propane tanks are only 1/4 full even when filled to max capacity.

Whoa that's something I didn't realize. I always had the intuition the speed was faster in denser materials but you're right that pressure doesn't matter.

The temperature difference does make sense for the same reasons here though!

It does depend on density because density, pressure, and temp are all related. https://en.m.wikipedia.org/wiki/Ideal_gas_law

For an ideal gas. Get close to the triple point of the gas and you better upgrade your equation of state

I think it's just relativity. After all, the gas in the Earth's atmosphere is traveling 29.78km/s relative to the sun (~Mach 85). Inside of the nozzle it doesn't really matter that it's traveling supersonic relative to the air outside the nozzle until it leaves the nozzle.

I don't think the difference in speed of sound will have much effect in any case.

"The speed of sound does not depend on pressure, only temperature"

Of an ideal gas

It sounds like you just described "choked flow"[0], where reducing the downstream pressure no longer increases flow velocity. It's been many years since I learned it, but I think this occurs at only about 2:1 pressure ratio across the venturi. If I'm remembering that right, just letting the air out of your tires would result in choked supersonic flow.

[0]https://en.wikipedia.org/wiki/Choked_flow

Edit: I got excited to reply before actually reading the wiki I linked. Looks like I was close, with pressure ratios between 1.7 and 2.05 resulting in choked flow, depending on the gas.

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