Volume of air in tank at a given pressure/temperature

[icestac]

The only other thing I can think of would be to get the tank measurements (height + diameter) and composition (AL/Steel) and compare it to other known tanks and that will get you close.

TDL Cylinder Specifications

~Jeff

 

[Rick Murchison]

What I was really looking for is something like take the volume of an empty cylinder and multiply it by the pressure/temperature to figure out exactly the volume of gas in your cylinder.

Well, now, for simplicity, let's start with the European system.
Assuming a constant temperature...
As tank size is rated in water volume, and pressure measured in bar, 'tis simply a matter of multiplying the tank size times the pressure.
A 10 liter tank filled to 200 bar holds 2000 liters...
To do the same with the Imperial system, the most convenient way is to first calculate the interior volume of the tank... for an AL80 that's 77.4 CF divided by 3000/14.7 ATA, or 0.379 CF. To find out how much you can get out of that tank at 1 ATA all you need to do is take the gauge pressure in psi divided by 14.7 and multiply that by 0.379 to get the answer.
So, at 2000 psi, it's (2000/14.7) X 0.379 = 51.6 CF
- or -
you can figure out that 0.379 CF = 10.7 l
and 2000 psi = 136 ATA
so, using the European method, the tank would hold 10.7 X 136 = 1455 l, and 1455 l = 51.5 CF
---
Glad I could help
Rick

 

[wve]

Wouldn't you figure it this way (assuming standard fill and temperature):

Tank pressure rating / Tank volume = Tank pressure-volume ratio. So in your case:

2400 psi divided by 85 CF = 28.2 psi per CF.​

Now, to find how the volume of air in your tank, divide the psi on your gauge by the tank pressure-volume ratio of your tank. In your case again:

2000 psi on your gauge divided by 28.2 = 70.9 CF in your tank.​

What becomes confusing to me is when you overfill. If you overfill to 2640 psi, then you increase the P/V ratio to 31 psi/CF. But then what happens?

Do you maintain that ratio until the tank is empty? Or once you use the overfill and are back to 2400 psi, do you revert back to the standard pressure/volume ratio of 28.2 psi/CF?

For practical purposes, it may not matter because you are only talking about a 10% difference which may be within the margin of error of the gauges, temperature shifts, etc. But it is an interesting question you ask.

Addendum: Rick must have posted his reply while I was typing mine, so I hope this doesn't appear that I am taking issue with him. I think we are actually addressing slightly different questions that you ask.

 

[Rick Murchison]

What becomes confusing to me is when you overfill. If you overfill to 2640 psi, then you increase the P/V ratio to 31 psi/CF. But then what happens?

The interior volume of a tank is (essentially) constant. Therefore the P/V ratio (where V = the volume of gas in the tank at 1 ATA) is constant.
Tanks are generally rated at some overfill pressure...
A LP 85 holds 85 CF at 2640 psi. At 2400 psi it holds about 77 CF.
An AL 80 holds 80 CF at 3100 psi; 77.4 CF at 3000 psi.
An old steel 72 holds 72 CF at 2500 psi (even more than the 2250 + 10%) - that is 71.2 CF at 2475 and a little under 65 CF at the rated tank pressure of 2250 psi.
And all these numbers are dependent on the assumption that everything's being measured at the same temperature and that 1 ATA is 14.7 psi and that the ideal gas law is accurate and that the tank is inelastic - none of which are quite right, eh?
Rick

 

[wve]

And all these numbers are dependent on the assumption that everything's being measured at the same temperature and that 1 ATA is 14.7 psi and that the ideal gas law is accurate and that the tank is inelastic - none of which are quite right, eh?

Right.

It is fun trying to do the math, but unless you are a "numbers person" (which I am not), it can get tricky. Sometimes the math can look right, but if based upon faulty assumptions, is nevertheless wrong.

So I try to understand the principles.

Well, that is easier said than done, especially when there are multiple variables which themselves are not constant. Such as when you consume the gas in a tank, and the pressure decreases, and the tank contracts, and temperature cools, and the gas contracts. When all that happens, the P/V ratio must change, but is it enough to matter? Probably not. If you really gotta know, you probably need to dust off the calculus textbook, but I'm too old to care THAT much.

So that is when I start looking for a "rule of thumb" -- which is where I stumbled upon the pressure/volume ratio as a guide to figure what volume of air is left in a tank when I know the tank's volume and the psi on the gauge. It works for "standard" tanks and conditions. The problem arises when you start changing things -- like overfilling. Now which ratio do you use -- the one for the "standard" fill pressure or the one for the "overfill" pressure?

I guess one can take his/her pick. At the end of the day, just fill my tank all the way full so I can spend more time underwater instead of doing math.

 

[greg98072]

This is the formula I use: Tank pressure X Tank size/Rated pressure

Example for LP85: 2200 X 85/2640 = 70.83

2900 X 85/2640 = 93.37


To make it easy use the calculator on your cell phone and write the formula on your certification card.

 

[Papa_Bear]

Percentage is the easiest for me! 95cft tank at 2450psi equals 100% full or 95cft. every 245psi or 10% means 10% less than full or 85.5cft and so on in either direction. It really is the same formula just a decimal point thing 1225psi=42.5cft etcetera!

 

[SparticleBrane]

LP95s are full at 2640, not 2450.

 

[sheck33]

I believe that would be physics at work

Correct.

 

[sheck33]

This is the formula I use: Tank pressure X Tank size/Rated pressure

Example for LP85: 2200 X 85/2640 = 70.83

2900 X 85/2640 = 93.37


To make it easy use the calculator on your cell phone and write the formula on your certification card.

Or better yet, understand the equation and just memorize it.