Originally Posted By: kallog
Hi yea I learnt a few things off this. But I still don't like those explanations :P Seems to me a rarified gas would approach being ideal.

They do, in a way. Because physical interactions are rarer, they flow more readily and experience less back pressure. The end effect of this is an increase in the speed of sound, and thus they don't get choked until much higher velocities.

The speed of sound, BTW, is higher at lower pressures.

Originally Posted By: kallog
Also not sure why it really has to go at the speed of sound. I think that's only an upper limit when you have way too much force pushing it. For a bottle rocket I bet there's no speeds of sound happening.

Absolutely! The speed of sound is simply the maximum speed that a gas will travel at through the narrowest part of whatever it is flowing through. If you have insufficient force, too much friction, etc, you will not get to the speed of sound.

However, in pauls device you will reach the speed of sound quite readily. His ~6000N of pressure force is more than ample to accelerate air to that speed.

Bottle rockets are not a really good comparison though - your expelling water (a liquid) not a gas, so the physics are completely different. That said, flow of a liquid can be choked (and is choked at the speed of sound). However, the speed of sound in water is quite high (~1500m/s!), and I highly doubt a water bottle could support the pressure you would need to achieve that speed.

Originally Posted By: kallog

I tend to dislike engineering equations (despite using them every day ;), because of exactly these problems. They're usually simplifications that only apply to special cases. No room for doing your own thing, and very bad for extreme thought experiments.

I don't think it would be fair to call these equations "engineering equations". They are the physical equations which describe the forces involved in the flow of a non-ideal gas. Engineers use them, not because they are simplified versions of reality, but rather because they are accurate representations of reality. You'll see those equations used throughout the physical sciences as well - not because they are simplified, but rather because they describe realty.

Originally Posted By: kallog
Perhaps you should tell Paul directly that Ve isn't zero anymore wink

I get the feeling he doesn't read my posts anymore...