[EthanNino]

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)

Argon            319
Helium   1007
Krypton   221
Xenon   76
Hydrogen   1270
Nitrogen   349
Oxygen   326
Carbon Dioxide   267
Sulfur Dioxide   201
Ethylene   327
Methane   446
Propane   258

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 = 100Pascals

http://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?

Summary:

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!

[curiouscat]

n = 179129.7
m = 44782.4g
m = 44.8kg He?

How? I get 716 kg.

m=M.n with M=4

I could be wrong.

[curiouscat]

2.Does Helium mix evenly with air in a low pressure environment?

I think, yes.

3.Would it be economical to fill a low pressure tunnel with Helium? Leaks?

Hard to say. It is an engineering problem. Even with a 30 feet vacuum distillation column or a CVD lab reactor leaks can be a big pain especially at sub torr levels.

You'd have to worry about air leaking in, equipment degassing etc.

4.Will an electric compressor work in Helium, or Helium spiked air?

It should work.

If you ask me, the ~2x theoritical improvement in limiting speed is not worth the hassle of He. 800 mph is a good speed as it is. If he can  achieve it. Count me skeptical. If he gets this commercially successful, even in 10 years, I'll buy you dinner.

[EthanNino]

I get 716 kg.

m=M.n with M=4

Ahh, see I divided by 4 instead of multiplied. I knew I made a mistake somewhere!

Hard to say. It is an engineering problem. Even with a 30 feet vacuum distillation column or a CVD lab reactor leaks can be a big pain especially at sub torr levels.

You'd have to worry about air leaking in, equipment degassing etc.

The original design parameters called for a 100 Pascal pressure inside the tube, which admittedly seems very low to me as well. The goal was to have a similar pressure of 15,000m altitude, to reduce the drag on the capsules. According to the plan, the walls of the tube would be made out of steel, but I know what you mean about Helium's habit of leaking out of containers. I looked this up on Wiki:

Helium leaks through cracks should not be confused with gas permeation through a bulk material. While helium has documented permeation constants (thus a calculable permeation rate) through glasses, ceramics, and synthetic materials, inert gases such as helium will not permeate most bulk metals.[93]

Which may be problematic if the tube is to have any window sections, as it is often depicted. I'm not quire sure what you mean by sub torr levels, does that mean the leakage is worse if there's a low pressure on the inside or outside?

In addition, the plan mentions that aerodynamic drag increases with the square of the speed, so even if the capsule wont travel any faster with He, they may need less energy to travel, I think?



I don't want to embarrass myself twice in one night, but the Goodyear blimp has an internal volume of 8030m^3, so I calculated the mass of He in it:

V = 8030m^3
T = 68 F
P = 101.3kPa

http://www.chemicool.com/cgi-bin/gaslaws.pl
PV = nRT

n = 333752.9
m = 1335 kg He

The whole tube, back and forth would only need half the amount of He as the Goodyear Blimp at sea level, and 1/4-1/3 as much if half He and half air. So it's not a whole, probably enough to replenish it periodically without much hassle. With such a low pressure, would Helium still leak out as quickly as it normally would? Though I deplore the thought of wasting Helium for any reason, I think it might not leak as rapidly with the negative pressure acting on the tube.

In addition to my other questions, do you happen to know if Helium is better or worse at Electrohydrodynamic propulsion than regular air? Like if you had a vessel full of Helium and a lifter inside of it, would it even take off?

[curiouscat]

Which may be problematic if the tube is to have any window sections, as it is often depicted. I'm not quire sure what you mean by sub torr levels, does that mean the leakage is worse if there's a low pressure on the inside or outside?

In a vacuum you have to worry about air leaking in. The lower the abs pressure you desire the worse is the problem.

Will he weld it all? Will he have flanges & gaskets?

With such a low pressure, would Helium still leak out as quickly as it normally would?

Wrong worry. Worry about air leaking in.

[billnotgatez]

The Goodyear Blimp gets refilled with Helium regularly because the Helium seeps out through the skin.
The Goodyear Blimp gets purged of air regularly because the air seeps in through the skin.
The purging process includes a purification process so as to leave the helium inside and only remove the air. That purification process is not trivial.

The Goodyear blimp is kept at a slightly higher pressure than the outside air which is the opposite of the tunnel you are discussing. But, I think that some helium will seep out of the tunnel anyway, but how much I am not sure. By far the most pressing problem is how to remove air inside the tunnel without losing Helium.

See also this discussion we had a little while ago, where we talk about helium, hydrogen, and carbon dioxide in air. Although only some of it discusses how gasses mix, you can pick out how the Helium is likely to mix with the air in a horizontal tunnel versus a vertical tunnel.
http://www.chemicalforums.com/index.php?topic=69975.0
 
Right now the Goodyear Blimp and many other users of Helium are having supply problems due to the shortage of Helium availability. There are expectations that this shortage may be alleviated with future foreign sources.

[EthanNino]

In a vacuum you have to worry about air leaking in. The lower the abs pressure you desire the worse is the problem.

Will he weld it all? Will he have flanges & gaskets?

He said they would be welded together using an orbital 'welder':


I think the way it's going to be built is in large prefab sections that can be transported on top of the completed sections of tube. They would put the next tube section in place, weld it, and then use it to transport other sections on top of. Sort of like how railroad is built, but yeah, he said they would be welded together. I'm assuming the tube is already thick walled, and the welds relatively leak proof to handle the 100 Pascal air pressure.

Wrong worry. Worry about air leaking in.

Yeah, the surface area of the tubes are gigantic. If you pumped the increased air/Helium mix out of the tube, and pumped the Helium back in, would that work? It would maintain a low pressure, while reserving the Helium.

The Goodyear Blimp gets refilled with Helium regularly because the Helium seeps out through the skin.

True, but I think that the walls of the Hyperloop would be more impermeable to Helium seepage than the skin of the Goodyear blimp. From what I understand, Helium seeps out of ceramics, glasses, and synthetic materials, but not so much through inert metals.

[curiouscat]

Yeah, the surface area of the tubes are gigantic. If you pumped the increased air/Helium mix out of the tube, and pumped the Helium back in, would that work? It would maintain a low pressure, while reserving the Helium.

How'd you separate them?

[EthanNino]

Yeah, the surface area of the tubes are gigantic. If you pumped the increased air/Helium mix out of the tube, and pumped the Helium back in, would that work? It would maintain a low pressure, while reserving the Helium.

How'd you separate them?

I figure that in order to maintain the 100 Pascal pressure if there are leaks present, a large amount of air/Helium mix are going to need to be pumped out. When it's pumped into a higher pressure container (higher than the 100 Pascals of the tube), the Helium can be separated from air more easily, and recycled back into the tube, and the same amount of air that seeped in, can be pumped back out:

Probably very energy consuming, but the Hyperloop is supposed to generate a lot more electricity with solar panels than is actually needed by the cars, so some of it could be used for this. I anticipate something similar will be needed even if there is no He in the system, just to maintain the same pressure with leaks present. The introduction and separation of Helium from air would be the only additional steps I think, and maybe the occasional topping off. From what previous people said, the tube will have a lower abs pressure, so the Helium probably wont leak out as much as the air leaks in, which in itself keeps the He from leaking out.

[curiouscat]

I anticipate something similar will be needed even if there is no He in the system, just to maintain the same pressure with leaks present.

Vacuum Pumps. No separation. A different ball game.

The introduction and separation of Helium from air would be the only additional steps I think, and maybe the occasional topping off.

Understatement of the year. How big / expensive do you think a Helium plant is. I doubt your economics will work out.

I could be wrong. I'd love to see some cost estimates.

[EthanNino]

Yeah, I did understate the complexity of separating Helium and air. One way they do it now is by liquefying air and collecting the Helium as it has a much lower freezing point than any of the gasses in air. It's expensive, and doesn't yield a whole lot of Helium, but that's because there isn't a whole lot of Helium present in air. In this closed system, half to all of the gas would be He, minus the air that would leak in. So instead of liquefying a boatload of air to get a tiny bit of He, you would only need to liquefy a relatively small portion to separate out the Helium. It wouldn't be an industrial process, to get as much He as fast as possible, but a gradual one to keep up with small leaks in the tubes, so I don't think a particularly large/expensive separation plant will be required.

Truthfully, I have no idea how much it would cost, lol, it's difficult to anticipate how much air would leak into the system without knowing how well it will be constructed. Elon has a good track record when it comes to quality, but yeah. I'll keep refining the cost estimation best I can with the information given.

The way I see it, it uses 1/2 to 1/4 as much Helium as the Goodyear blimp for both tubes with Helium, uses materials that are MUCH more impermeable to He than the skin of the Goodyear blimp, and at a lower pressure. Even with such a large surface area, I figure the rate of leaking to be small, small enough for a small plant to handle the separation. This is for a multibillion dollar transportation system, so proportionally it may take up only a small fraction of the total cost, and make up for it in increased speed of transit/saved energy requirements with a lower speed of sound.

[curiouscat]

Yeah, I did understate the complexity of separating Helium and air. One way they do it now is by liquefying air and collecting the Helium as it has a much lower freezing point than any of the gasses in air. It's expensive, and doesn't yield a whole lot of Helium, but that's because there isn't a whole lot of Helium present in air. In this closed system, half to all of the gas would be He, minus the air that would leak in. So instead of liquefying a boatload of air to get a tiny bit of He, you would only need to liquefy a relatively small portion to separate out the Helium. It wouldn't be an industrial process, to get as much He as fast as possible, but a gradual one to keep up with small leaks in the tubes, so I don't think a particularly large/expensive separation plant will be required.

Truthfully, I have no idea how much it would cost, lol, it's difficult to anticipate how much air would leak into the system without knowing how well it will be constructed. Elon has a good track record when it comes to quality, but yeah. I'll keep refining the cost estimation best I can with the information given.

The way I see it, it uses 1/2 to 1/4 as much Helium as the Goodyear blimp for both tubes with Helium, uses materials that are MUCH more impermeable to He than the skin of the Goodyear blimp, and at a lower pressure. Even with such a large surface area, I figure the rate of leaking to be small, small enough for a small plant to handle the separation. This is for a multibillion dollar transportation system, so proportionally it may take up only a small fraction of the total cost, and make up for it in increased speed of transit/saved energy requirements with a lower speed of sound.

You sound optimistic.

I'm totally not. Time will tell.

To me this has all the red flags of hype: A grand proposal without an iota of actual prototyping. A fairly fluffy report (as far as engineering proposals are concerned) with cool pictures but little nitty gritty design or basis for costing. 

Promising the stars without having any pilot unit running. Huge number of engineering projects that were abandoned,  were due to unanticipated problems discovered during test-runs.

Even his potential ridership numbers seem drawn out of a hat. A little more humbleness in an exploratory report would work better.

Devil's always in the details. 

[Arkcon]

This is a pretty good thread for our forum, regarding the gas laws, and some chemical engineering.  But the whole concept, is like curiouscat: said, is poorly thought out, and poorly planned.  Consider this thread in another forum that's also a favorite of mine -- they discuss many of the engineering and planning topics: http://boards.straightdope.com/sdmb/showthread.php?t=699329

[curiouscat]

This is a pretty good thread for our forum, regarding the gas laws, and some chemical engineering.  But the whole concept, is like curiouscat: said, is poorly thought out, and poorly planned.  Consider this thread in another forum that's also a favorite of mine -- they discuss many of the engineering and planning topics: http://boards.straightdope.com/sdmb/showthread.php?t=699329

To  me the amazing part is how the media buys into the whole concept hook line and sinker. I think we need a more healthy dose of skepticism in all this. Nothing wrong with an out of the box idea but let's take things in stages. Let someone fund, say, a ~$20 million scaled down prototype first. Let's test the drag, vacuum leakage, compressor capacities and then we are on a stronger footing to say something about if or not a grand project may work.