The tolerances on each part must be very tight. If there is a single flaw in one part, the whole vacuum fails. The challenges become exponentially greater as you scale up the diameter of the pipe, since the force on the pipe is proportional to the square of the radius. The LHC had a 50mm diameter pipe, the hyperloop proposes an 8+ foot diameter. You do the math.

When you said that you worked on the LHC for several years - what was your role, and how were you involved with the vacuum system? Because your answers show a serious lack of understanding.

First, part tolerances are not a particularly important issue with engineering of high vacuum systems (sealing is effected by compression of gaskets, usually soft stainless steel gaskets for UHV systems).

Secondly, the difficulties in maintaining a large UHV system is usually related to "outgassing", from multiple surfaces and/or material imperfections, and are rarely due to "a single flaw in one part".

Thirdly, you are using the word "exponentially" wrong, even in the context of your flawed claim which is addressed below.

Finally: "the force on the pipe" is not, in a meaningful sense, proportional to the square of the radius. The forces in the pipe wall are proportional directly to the radius (formula is stress=pressure*radius/thickness), if it was otherwise pipe thickness would grow as the square of diameter and large pressurised pipes would be physically impossible.

Happy to do the math for you when you need it, best to leave it to the experts.

Regarding your first point: from my experience (working on physics experiments that depend on vacuum <10^-11 torr), the construction of the knife edge that seals against the gasket is fairly important - any chips or imperfections and the part is garbage. Also do people really use stainless for gaskets? I've always used (and seen other people use) copper, stainless sounds like a huge pain to torque down on.

I doubt UHV experience is relevant here though - at 100 torr you can probably get away with simple o-ring seals. And outgassing doesn't matter: even isopropanol has a vapor pressure of only 40 torr.

Edit: The hyperloop design is at ~1 torr, not 100. Still, I'd imagine outgassing is not a huge issue.

Just FYI - hoop stress as you've quoted it assumes a thin walled cylinder. I haven't worked on the LHC so don't know the dimensions; however, this assumption is really only valid for D/t > 20 or so before solutions diverge at which point the interaction becomes more complex than R/t.

The Hyperloop will operate at about 15 psi pressure differential maximum (i.e., one atmosphere).

The Alaska Pipeline is certified to operate at 1,180 psi.

It's not a problem, and minor leaks are not a problem, either. A leak that would stop a particle accelerator dead in its tracks will just make a hyperloop operate at slightly lower efficiency. Plus you can always just run the pump (any practical design will doubtless have the pumps running continously to make up for leakage, just as many ships and buildings have continuously-running bilge and sump pumps).

My personal opinion is not that it can't be done, but that it's financially impractical given then huge maintenance costs compared to conventional high speed rail system.