How to convert tanks sizes from imperial to metric

[acreichman]

I originally learned to dive in imperial units and later switched to metric because I find them easier to use but one aspect has troubled me. How do I take the imperial tank measurements I know and convert them to metric capacity? I've done some calculations myself with my HP100 tanks (Worthington X7-100 if it makes a difference) and gotten one answer, then looked at charts I think are official and gotten 3 different answers for the same tank.

This is the answer I think is most correct:
100ft^3 = 2832L
3442 psi = 237 bar
2832L ÷ 237 bar = 11.94L @ 1 bar

I think 11.9L is the answer to my question. Some spec sheets list the Worthington X7-100 as having an actual capacity of 99.5ft3 but using that value gives 11.89L instead of 11.94L. Those are close enough that I’ll call them the same and round both to 12L to make the math easier.

Where I start to get lost is when I look for tank specifications. I’ve found multiple spec sheets and none of them agree with the answer above.
The pinned post in this forum from @tmassey (which is amazing, you're a hero for putting it together), lists the internal volume as 12.2L.

Here’s a chart from Faber or XS Scuba (who sold my tank) that lists 12.9L:

(https://static1.squarespace.com/sta.../1587509035732/Faber-Steel-Cylinder-Specs.pdf)

I also found this chart, which is supposed to be specifically about Worthington tanks and has it at 11.6L:

(https://static1.squarespace.com/sta...88828531/Worthington-Steel-Cylinder-Specs.pdf)

These charts seem official but they disagree by more than 10% and neither of them agrees with the math I did first. If tank listings in imperial were off by that much it would be a difference of more than 350 psi. So now I have 4 different answers, ranging from a low of 11.6L to a high of 12.9L. I feel like I've gone down a rabbit hole and the actual answer must be simpler than I'm making it. If somebody could tell me what the right answer is, and how they know it's right, I'd be very grateful.

 

[Dive Concepts]

Thanks for sharing this amazing Information.

 

[Bob DBF]

I feel like I've gone down a rabbit hole and the actual answer must be simpler than I'm making it. If somebody could tell me what the right answer is, and how they know it's right, I'd be very grateful.

If you would like another rabbit hole look into the the compressibility factor of air at high pressure. You are treating the problem as one would an ideal gas, air isn't.

Once you wander that rabbit warren, get back to the land of "good enough" to do your planning.

 

[Angelo Farina]

Is not the exact capacity of the tank engraved on it, as on all of my Luxfer and Faber tanks?
My understanding is that the law mandates the manufacturer to engrave the real capacity and weight on each tank.
And they differ quite substantially for tanks nominally identical.
I and my wife own two Aralu twin tanks, each composed of two Luxfer alu bottles.
So in total 4 of them.
They all show different values both for weight and capacity. The difference between the smallest and the larger is close to 10%, and this among a population of just 4 samples, all of the same manufacturer and of the same year.
So in your case I would not worry too much at the "nominal" capacity.
If you want to know the exact capacity of your tank, proceed as follows:
1) empty the tank
2) remove the valve
3) measure the weight with a digital scale
4) fill entirely the tank with clean water
5) measure again the weight
6) empty the tank and leave it drying before mounting the valve (a hose carrying dry compressed air makes this faster).
The difference in weights, in kilograms, will be the tank capacity, in liters.
Still I think that this value should be engraved on the tank, alongside with the weight. Look carefully at those markings...

 

[Angelo Farina]

PS: if you do not like the idea of flooding your tank with water you can use compressed air, again measuring weight with tank empty and full.
But in this case the calculations are much more complex, as you need to take into account the pressure, the temperature and the compressibility factor.
But if what you want to know is not the capacity of the tank, but the real amount of air contained in the tank at a given pressure and temperature, you get this info easily: just multiply the weight difference, in kg, by 1190 and you get the air volume in liters at 1 bar and 20°C.

 

[tbone1004]

@Angelo Farina not required in the US.

@acreichman like @Bob DBF said, you forgot about compressibility factor which is a very real thing. If the manufacturer has charts published then use the charts, they will be far more accurate than any math you can do. In addition to using the z-factor, also remember that scuba tanks are called out by their nominal capacity and not their actual capacity.
If Worthington says they're 11.6 then they're 11.6 +0.1L or so. They are most definitely not as big as the Fabers which you can see by having the same diameter, but are about 7cm shorter. Your math got you to 11.94L but you didn't use the Z-factor which at 3442psi and room temperature is about 5%, so 11.94/1.05=11.5L though with some rounding differences somewhere 11.6L is perfectly reasonable.

 

[scubadada]

DGX has a nice article on their website Calculating SCUBA Cylinder Capacity | Dive Gear Express® Includes tables

 

[tmassey]

I feel like I've gone down a rabbit hole and the actual answer must be simpler than I'm making it. If somebody could tell me what the right answer is, and how they know it's right, I'd be very grateful.

Well, you now understand exactly why I sat down and made that spreadsheet. And like others have mentioned, it was actually the DGX article on compressibility factors that totally forced me to do the math from first principles.

The true idea of what a scuba tank holds requires three factors: one, the water capacity of the tank; two, the pressure of the tank (which also implies temperature); three, the contents of the gas. Only when you specify all three factors can you truly understand the “capacity“ of a tank.

And +1 to @Bob DBF: in the end, it’s all an approximation, and you just have to get as relatively close as you can without killing yourself in the process. Not only is it “measure with a micrometer, mark with chalk, cut with an ax“, but if you need any kind of level of precision, you’d be much better off just reducing your turn pressure or whatever by 100 psi / 7 bar and calling it good.

 

[acreichman]

DGX has a nice article on their website Calculating SCUBA Cylinder Capacity | Dive Gear Express® Includes tables

This was a very helpful read, thank you.

@tbone1004 @tmassey both of your posts were very helpful, even if I didn't get the simple answer I was hoping for. At this point, I think it makes sense to clarify why I want this information and maybe that will help me figure out what to do. I have a transmitter on my tank and I download my dives, including gas usage, into MacDive, which then tells me my gas consumption rate. Gas consumption rate depends on volume consumed, which is tank dependent since transmitters can only report pressure changes. To make this work, I have to tell MacDive what size tank I'm using, and when I have it set to metric, it looks for a tank capacity in liters.

Here's the way I'm currently thinking about it, please correct me if I'm wrong. Compressibility factors exist because pressure vs. volume is not a linear relationship. MacDive, to the best of my knowledge, assumes volume and pressure have a linear relationship (I'm verifying this in the MacDive forums). More often than not, I'll start dives with full tanks. Given those 3 pieces of information, I should be able to figure out how much actual gas my tanks will have at full pressure (using the compressibility factor) and then work backwards from there to give MacDive a tank size that will be accurate at full pressure (but not at other pressure). If I do that, I'll get the most accurate information for the greatest number of dives. Does that sound correct?

 

[tmassey]

What you were describing is the definition, the very definition, of “measure with a micrometer, mark with chalk, cut with an ax“.

What that means is: you are trying to create a high-resolution measurement for your gas consumption. However, your gas consumption will change based on the temperature of the tanks, and therefore the temperature of the water; the type of gas inside the tanks; The pressure range that you use; and all of this in addition to the tank size that you need to put in, and none of which is included in a typical air consumption calculation in the first place!

Also, having a highly detailed record of precise gas consumption is not anywhere near as important as having a consistent record of relative gas performance. In other words, if your SAC rate is .63 or .61, the difference is meaningless. But if on a particular dive you used 20% more gas than you normally use — whatever number that actually is – that’s a lot more important to know. And you can create those relative statistics with sufficient accuracy even without a high precision measurement of the volume of your tanks.

To make things worse is the small variation in tank sizes between manufacturers, as you have found. So if you own your own tanks, then you are at least starting with a consistent starting point, even if you don’t know the proper value precisely. But if you’re using different tanks, such as rentals or a friend’s tanks, you’ll never really know the “true“ water capacity. So you’re foiled from the beginning.

But even if you had all of those details, you’re still going to be messed up by the variations in how you dive. Maybe there is a free flow at one point during the dive. Maybe you do a share air drill with somebody. Maybe it’s a bumpy bottom contour and you use a lot of gas in and out of your wing.

Basically, the level of precision you are striving for is a fool’s errand. You are extremely focused on one small part of a very complex formula, almost none of which you can directly control, and bemoaning the fact that you can’t get its precision to multiple digits.

I’m not kidding when I say that is exactly why I created that spreadsheet: I too was focused on specific tank capabilities, wondering what would be the “best“ tank. Once I delved into it and realized that not only is determining those characteristics precisely almost impossible, but that the variations only made a few percent difference, I was finally able to let go of that mindset.

The sooner that you realize that trying to achieve a level of precision greater than a few percent while engaging in scuba activities is nearly impossible, the happier you will be with the entire process!

ETA: While you are at it, think of it this way: Do you think you are the first tightly-wound Type A personality to enter the scuba diving hobby? I can tell you that you are not, because I’ve been doing this since 1992… and given that there are other tightly-wound people out there doing this hobby, and yet no one tracks any of that information at that level of precision, that might give you an idea of whether tracking it at that level of precision is actually necessary, or even what value it would have even if it could be done. Because if it were valuable to have that, there’d be a lot of us tightly-wound types beating on people’s doors so that we could get that information! The fact that we are not should give you a little bit of confidence that you don’t really need it.