Howdy! I'm new around here, and I've got a few questions about gasses mixing and pressure differentials.
Yesterday, Elon Musk revealed his Hyperloop plans to the world. The Hyperloop is basically a pneumatic tube transport system for people, that can travel 700-800mph, proposed as a cheaper and faster alternate to the current San Fransico-LA bullet train planned:http://www.teslamotors.com/sites/default/files/blog_images/hyperloop-alpha.pdf
He said he's currently to busy to make or even prototype it with Tesla and SpaceX to worry about, and he wants people's input on it if they see any room for improvement. I read the document, and cooked up a few ways to increase the top speed of the train cars. Here's an excerpt concerning the internal environment of the tube, people have speculated that the Hyperloop would be a vactrain (evacuated tube transport), when in fact it has a low internal pressure inside:Just as aircraft climb to high altitudes to travel through less dense air,
Hyperloop encloses the capsules in a reduce pressure tube. The pressure of air
in Hyperloop is about 1/6 the pressure of the atmosphere on Mars. This is an
operating pressure of 100 Pascals, which reduces the drag force of the air by
1,000 times relative to sea level conditions and would be equivalent to flying
above 150,000 feet altitude. A hard vacuum is avoided as vacuums are
expensive and difficult to maintain compared with low pressure solutions.
Despite the low pressure, aerodynamic challenges must still be addressed.
These include managing the formation of shock waves when the speed of the
capsule approaches the speed of sound, and the air resistance increases
sharply. Close to the cities where more turns must be navigated, capsules
travel at a lower speed. This reduces the accelerations felt by the passengers,
and also reduces power requirements for the capsule. The capsules travel at
760 mph (1,220 kph, Mach 0.91 at 68 ºF or 20 ºC).
From this, it seems as though the speed of sound is a potential barrier as wind resistance increases sharply close to it. I was thinking, the tube is kept at such a low internal pressure, only 100 Pascals, if it were partially filled with an inert gas with a higher speed of sound, would it also increase the upper speed limit of the train? I looked at this chart for reference:
Gas Speed of Sound (m/s)
Carbon Dioxide 267
Sulfur Dioxide 201
I figure from the above chart, Nitrogen has a higher speed of sound than Oxygen, and air has a speed of sound lower than Nitrogen, but higher than Oxygen, so it's like an average? If this is the case, would mixing the internal air with Helium greatly increase the speed of sound inside the tube? Or maybe even replacing it outright with pure Helium?
If so, than in such a low pressure environment, would the Helium mix with the air inside the tube, or separate out to the top? I know that increasing the temperature of a gas increases the speed of sound through it, so if it were heated up a little, would the gasses mix more thoroughly?
I'm pretty sure my calculations are off on how much Helium would be required, but here's what I did:
Radius = 1.115m (2.23 inner diameter)
Length = 1117360m (2 tubes side by side from LA to San Fran)
V = 4365836.8m^3
T = 68 F (sorry about Fahrenheit)
P = 100Pascalshttp://www.chemicool.com/cgi-bin/gaslaws.pl
PV = nRT
n = 179129.7
m = 44782.4g
m = 44.8kg He?
It seems like such a small amount to fill such a gigantic tunnel, even with the pressure so low. The Helium will probably all eventually leak out, but it just seems like such a small amount that it could be periodically replenished. The cars will have a compressor on the front to actively counter the 'Kantrowitz limit', so would it be able to run in Helium? It's an electric powered compressor, in fact the whole thing is solar powered, so I don't see any reason why it wouldn't work.
Another idea would be to actively decrease the pressure in front of the capsule, and increase it behind the capsule, so it would 'ride' a pressure wave. Just a slight differential. On average, the capsules would be separated from each other by a distance of 37km, so I figure that would be enough space to increase the pressure behind one car, and decrease it in front of the car behind it. I'm not sure if this would work though, the capsules are expect to way several thousand pounds depending if they're carrying cargo or people, so would a little pressure difference acting on the front and rear of the capsule help it along at all, or counter the Kantrowitz limit?
1.Will mixing Helium with air increase the speed of sound through it?
2.Does Helium mix evenly with air in a low pressure environment?
3.Would it be economical to fill a low pressure tunnel with Helium? Leaks?
4.Will an electric compressor work in Helium, or Helium spiked air?
5.Would a pressure differential across the capsule propel it, or counter the Kantrowitz effect?
6.Can the 'air hockey table' effect work with Helium?
I haven't taken a chemistry class in a while, so I apologize in advance for any misunderstandings. So many questions, sorry about that, but the Hyperloop has got me all worked up. Thanks for reading, and I look forward to your replies!