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I fill my tanks to 3600 psi. Go dive a cave. Turn the dive when the pressure reaches 2400 psi. Exit using exactly the same amount of gas.

What pressure do I have at the end of the dive?

for compressibility considerations, you need to know how much oxygen, nitrogen and helium are in your mix. you'll also need to know temperatures throughout the dive as well. and i believe that the benedict-rubin-webb equation is better than the van der waals equations, particularly for helium.

all told it comes to around 5% or less error, though, which is about 60 psi (out of 1200 psi) and roughly equivalent to a 15C or 27F change in temperature.

and that number should be swamped by the speed of your exit -- where i usually only take around 70% of the time to exit that i took going in -- which is 360 psi difference in this example or 6x the size of the compressibility issue.
 
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I just played with a Van der Waals Nitrox Blender, and looks like at 2400psi and less you actually end up with more cuft than calculated (about 103%) while at 3600psi the opposite is true (about 98%).

Which throws a new kink into figuring turn pressures with dis-similar tanks.
 
I stumbled upon this old thread, and being bored decided to do the math:

If you use the van der Waals equation, the answer is 1414 psi.

Assuming:
Tank size: Al80 = 11.3L
Gas (air), so a = 0.1358 [J*m^3/mol^2] and b = 3.64x10-5 [m^3/mol]
Temperature: 20°C or 293K

Not much of a cave dive on Al80s and air in 20°C water, but the principle stays the same...

You start the dive at 3600 psi (about 24.8 MPa), which gives you 113.3 moles of air. (Calculation)

At 2400 psi (16.6 MPa) you turn around, still with 80.6 moles of air, having consumed 32.7 moles. (Calculation)

To exit, you use the same MASS of air, so your consumption measured in moles stays the same: you exit the cave with 47.8 moles of air. This means a pressure of 1414 psi. (Calculation)

Online van der Waals calculators like this one: http://antoine.frostburg.edu/chem/senese/javascript/realgas.shtml give similar values.

I am NOT sure if the real life error is actually that large, somebody who knows more about this topic should please weigh in (or show me an error in my calculations)!
 
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I'm reminded of something Rick Murchison was fond of saying ... measure with a micrometer, mark with a laser, cut with an axe.

I'd be more concerned about the effects of flow ...

... Bob (Grateful Diver)
 
It's just a theoretical exercise really!

Also if you express the error as a percentage of a full tank it's only 7%, so pretty negligible if you account for all the other factors.

What's interesting to keep in mind though is that up to about 225 bar / 3300 psi you actually have a bit more air in your tank than you would expect if air behaved as an ideal gas, while above that you have less. In other words, filling your tanks above 225 bar would bring diminishing returns.

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I'm also in the camp of the gauges have variance in them which is usually only accurate to half of the marks, so in the US that's +_50psi, even great in bar gauges *+_5bar/+_72psi*. That's right about 1.5% of variance in the gauges which is what most are certified to. Since the gauges are off on the high side when full and the low side when at lower pressures that's exactly where you want the variance to be. Lower than thought when full and higher than thought at turn pressure.

Reasons planning in siphons is rather important, but when they're springing it's less of a concern. I can honestly say that I've never come out of a cave anywhere close to the actual 2/3's mark, I'm always a few hundred pounds over coming out due to the flow.
 
depends on the flow. Use 1200 to enter at Ginnie or Madison blue, you'll probably have 1900 left at the end of the dive because your ride out will only take 500 psi.
 
https://www.shearwater.com/products/teric/

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