Tank Mathematics

[The Kraken]

I think you are right. Thank you.

Edited.

Mea culpa . . .

the K

 

[Scared Silly]

Not to slag on the OP. But I find questions like this one to be very sad. This question is a simple fractions problem that most people get taught or should have been taught about in about 5th grade. And IIRC isn't this question also covered in a basic OW course as well??

 

[The Kraken]

Scared Silly,

You are correct in your observations, but when it comes to something new and alien to the human physiology, such as scuba diving, some people have a tendency to become confilcted.

I think that we, the members of ScubaBoard, serve a greater purpose to help educate rather than denigrate.

I'm quite happy when one of our own comes here and asks, for what many of us seems to be, the obvious, than go out and doe something reckelss and dangerous.

There is no such thing as a stupid question . . . and not all instruction is equal.

Let us mentor, not censure . . .

Safe dives . . . . . . . .
. . . safer ascents ! ! !

the K

 

[Diver Lori]

Written by a diving physicist friend of mine who prefers Internet anonimity......

--------------------------------------------------

SCUBA Tank Buoyancy
Name withheld, but this is copyrighted
25 Mar 01
The buoyancy of any given object in water is a function of the density of the water, the weight of the object, and the volume of the object. While the density of sea water is slightly greater than fresh water, there is very little density variation with depth within normal diving ranges. Since a SCUBA tank is essentially a rigid container, little change in volume will occur with changing internal or external pressure. Therefore the buoyancy of a SCUBA tank in a given type of water will be almost entirely a linear function of the weight of air contained.

The weight of air in a SCUBA tank is most closely related to the volume of air compressed into the tank. The weight of 50 cu. ft. of air is about 4.0 lb. - or about 1.0 lb for every 12.5 cu. ft. of air.
A 95 cu. ft. steel tank would contain 95 cu. ft. / 12.5 cu. ft. per lb. = 7.6 lb of air at its +10% rated pressure of 2640 psi. (2400 + 240 psi.)

An 80 cu. ft. aluminum tank would contain 80 cu. ft./12.5 cu. ft. per lb. = 6.4 lb of air at its rated pressure of 3000 psi

A 72 cu. ft. steel tank would contain 72 cu. ft. / 12.5 cu. ft. per lb. = 5.76 lb of air at its +10% rated pressure of 2475 psi. (2250 + 225 psi.)
It is often more convenient to relate the contents of a SCUBA tank to the pressure of its contents. A linear relationship exist between the pressure and the volume of the contents. To express the relationship between the pressure and volume of the contents of a given size SCUBA tank, a "Tank Factor" is computed. The Tank Factor is simply the rated volume of the tank in cu. ft. divided by the corresponding rated pressure of the tank in hundred psi. (include the 10% over pressure for steel tanks). For doubles, the tank factor is simply doubled.

For a 95 cu. ft. steel tank: 95 cu. ft. / 26.4 hundred psi. = 3.6 cu. ft. per hundred psi.

For an 80 cu. ft. aluminum tank: 80 cu. ft. / 30.0 hundred psi. = 2.67 cu. ft. per hundred psi.

For a 72 cu. ft. steel tank: 72 cu. ft. / 24.75 hundred psi. = 2.9 cu. ft. per hundred psi.
Since the Tank Factor gives us a relationship between the pressure and volume of the contents for a given size tank, we can use it to get the relationship between the pressure and weight of the contents. If we simply "convert" the volume in the Tank Factor to its equivalent in weight, we will have a new "Weight" Tank Factor that will allow us to compute the change in tank weight for a given change in pressure.
For a 95 cu. ft. steel tank: 3.6 cu. ft. per hundred psi. / 12.5 cu. ft. per lb. = .288 lb. per 100 psi.

For an 80 cu. ft. aluminum tank: 2.67 cu. ft. per hundred psi. / 12.5 cu. ft. per lb. = .214 lb. per 100 psi.

For a 72 cu. ft. steel tank: 2.9 cu. ft. per hundred psi. / 12.5 cu. ft. per lb. = .232 lb. per 100 psi.

So, to summarize:

We know that the weight of a given SCUBA tank is approx. a linear function of its contents.

We know that the weight of 50 cu. ft. of air is about 4.0 lb. - or about 1.0 lb for every 12.5 cu. ft. of air.

For a given size tank we have a Tank Factor that will tell us how many cu. ft. of air the tank contains for each 100 psi. of pressure.

For a given size tank we can compute a "Weight" Tank Factor that will tell us how many lbs. of air the tank contains for each 100 psi. of pressure.

So, knowing either the empty or full buoyancy characteristics of a given tank, we should be able to use the above relationships to predict its buoyancy with any given level of contents.


Pretty cool, huh?

Name withheld
25 Mar 01

 

[GuardTrash]

Hey no slag taken, I dropped out of school in the 4th grade...........

Thanks Diver Lori! Lots of good info there.

 

[*dave*]

And IIRC isn't this question also covered in a basic OW course as well??

No, typically not.

It's the conversion which seems to confuse people.

 

[aku321]

This question is a simple fractions problem that most people get taught or should have been taught about in about 5th grade. And IIRC isn't this question also covered in a basic OW course as well??

Its been a long time since I took my OW class so I really don't remember but I don't believe it was covered. Its been even longer since I was in the fifth grade! I love these questions dumb or not, helps me remember things I might have forgotten about.

Dropped out in 4th grade? Well see there is the problem, he didn't get the edumacation he needed...

 

[gwilki]

Depending on how exact you need to be, you should keep in mind that at least some 80 cu ft tanks are not really 80. They are 77. HP 100's are mostly 102.

 

[WD8CDH]

The math is simple, but it seems the physics isn't part of OW training any more.