RMV on Jacked Tanks

[Big Deal]

I have been noodling over this for some time. Hopefully, without sparking a debate on the practice of cave/over fills, my question simply put is this: how do you determine an RMV or SAC when using overfilled tanks? The formulas I have used in the past have you put in the tank volume, and amount of PSI used, but I believe those formulas assume you are not boosting the tank above its service pressure. If, however, I fill my LP 85s to a PSI above their rated service pressure (2,400) there is going to me more cft air in there than the 85 stamped on the tank. Consequently, what tank size should I use when attempting to determine RMV if I were to dive with jacked up/cave filled tanks? How do I determine how much CF of air my LP tanks will hold when filling above their rated service pressure?

Thanks

[renoun]

You'll determine the constant between pressure and volume, in cubic feet per psi, by using the volume and the pressure the tank it is rated at. Once that is known you can calculate the actual fill volume at the actual fill pressure whether it is more or less than the rated volume.


Both Bob and Lamont have written pretty good explanations of how to do the math. You can come talk to Bdub about it in person on Monday.

[lamont]

its always:

cu ft used = cu ft tank * ( psi used / psi service pressure )

if you start with a 3500 psi filled lp104 and get out of the water with 1500 psi you just figure out the psi you used:

3500 - 1500 = 2000 psi

then plug that into the formula above, which doesn't care if the 2000 psi came off overfilled tanks or not, 2000 psi used is simply 2000 psi used:

cu ft used = 104 * 2000 / 2640 = 78 cu ft

[spatman]

This might help:

http://divenerd.com/sac-rmv/

[squid509]

the math will be still be correct if you use an over filed tank just make sure you use the correct rated capacity and rated pressure
be careful with LP tanks most manufactures rate the capacity based on the higher "+" rating of 2640psi
example

a LP95 @ 2640 = 93.3 ft3
LP95 @ 2400 = 84.8 ft3

http://www.xsscuba.com/tank_steel_specs.html

[Big Deal]

Thanks Sqid, I had assumed I needed to bump up the tank size for the purpose of doing the math. However how do I determine the amount of air in the tank at any given pressure? Again I'm assuming its a simple ratio so that if a LP 85 holds 85 ft3 of air at 2640 (a ratio of 31 psi = 1 ft3) then it holds 112 ft3 at 3500? Thanks for the links - good info.

Spatman, I use your site regularly. It's a great resource.

[squid509]

you math looks correct
but i let computers do my math for me less chance i get it wrong

[lamont]

Thanks Sqid, I had assumed I needed to bump up the tank size for the purpose of doing the math. However how do I determine the amount of air in the tank at any given pressure? Again I'm assuming its a simple ratio so that if a LP 85 holds 85 ft3 of air at 2640 (a ratio of 31 psi = 1 ft3) then it holds 112 ft3 at 3500? Thanks for the links - good info.

Spatman, I use your site regularly. It's a great resource.

Its not perfectly linear because of issues with the compressibility of non-ideal gasses, but those are on the order of a few percent, which is much less than the error your SPG.

For all practical purposes if you want to know your starting cubic feet you should just use the ratio.

You've also nearly derived tank factors there. Your 31 psi = 1 ft3 ratio can be converted into 3.2 ft3 / 100 psi which is the tank factor of an LP85 -- that is useful because it lets you convert between every 100 psi on your SPG into ft3 in your tank (and you can compare tank factors to determine which tanks are actually larger volume even though they might have different service pressures)

[kdupreez]

Practically for us, the whole "ideal gas law" when it comes to gas compressibility (i.e. van Der Waals) mostly applies with regards to partial pressures of gasses when you mix them, but even then, the biggest factor is really temperature and you can ignore the van der waals deviation for the most part, because gas heats up as it compresses and the compressibility factors become a wash.

To us as divers, its not practical to include "ideal gas laws" for volume calculations in tanks..

The biggest factor with the reality of gas laws that we as divers really should care about is temperature. especially if you take the fairly high to very low temp swings we have here the minute you stick your tanks in the water.

you might have calculated you have 100cft on the surface, but the minute you jump in the water, your tank cools down by 200psi and then you have like almost 6cft less in your tank..

So, your formulas will work fine. just keep in mind that your tank volume at 85 degrees in the sun will be different at 47 degrees in bottom of the puget sound…

so don't think 5min into your dive "HOLY crap, I breathed 10cft in 5min??".. your tanks probably just cooled down..

Or even worse, jump in the water, check your cooled down pressure and after the dive and after 1hour in the sun, then check SPG again before the next dive and use the high temp gas pressure and calculate you have a 0.35 SAC/RMV/SCR on previous dive..

As for tank factors, yes your LP85 tank is 3.2, but for practical reasons, I'd just use a TF or 3 for rough estimations.. it makes for MUCH easier calculations plus theres some conservancy built in.

but if you are calculating RMV/SAC/SCR then rather use the full ratio of 85/2640 * psi used

[lamont]

Practically for us, the whole "ideal gas law" when it comes to gas compressibility (i.e. van Der Waals) mostly applies with regards to partial pressures of gasses when you mix them, but even then, the biggest factor is really temperature and you can ignore the van der waals deviation for the most part, because gas heats up as it compresses and the compressibility factors become a wash.

To us as divers, its not practical to include "ideal gas laws" for volume calculations in tanks..

The "ideal gas law" is PV=nRT which is the linear one that we use in diving. There are a whole collection of non-linear gas laws that try to model the intermolecular forces in a gas which are referred to as "real" gas laws. There isn't just the Van der Waals equation of state, but also the Beattie-Bridgman model or the Benedict-Webb-Rubin models. However, it isn't necessary to include any real gas laws for volume calculations in tanks, or for mixing, the ideal gas law works fine.

As for tank factors, yes your LP85 tank is 3.2, but for practical reasons, I'd just use a TF or 3 for rough estimations.. it makes for MUCH easier calculations plus theres some conservancy built in.

but if you are calculating RMV/SAC/SCR then rather use the full ratio of 85/2640 * psi used

Depends on the fitness for purpose. If you're doing mental math in the water, 3 is certainly better, but my physics teacher in high school taught me to carry significant digits over to the end of the calculation. And if I'm converting from 600 psi / 10 min / 4 ata to SAC rates then using 3.0 gives me 0.45 cu ft / min, while using 3.2 gives me 0.48 cu ft / min, and 'rounding' to 3.5 instead gives me 0.52 cu ft / min, which isn't a lot but if I'm going to be planning consumption rates, the latter is definitely more conservative. The conservative direction of rounding always depends on what you are doing with it.