Pressure / Volume Formula

[Mechanic79]

I'm no scientist or mathematics professor so please help me out here. (or english for that matter:-)

I think this can help in two areas.

1. Filling smaller pb tanks from a SCUBA tank

2. buying the correct size tank in the first place.

Here is what I would like to know.

I have:
1. 68cubic inch 4500 PSI tank
1. SCUBA 120 cubic foot 3500 PSI tank

12"x12"x12" = 1728" ?

4500psi / 68ci = 66.17647 PSI per cubic inch?

EXAMPLE A:
Does a 68ci 3000 PSI tank have more shots than a 68ci 4500 psi tank if both are filled to only 3000 PSI?

EXAMPLE B:
How many fills can I expect from a 120 Cubic Foot 3500 PSI tank filling a 68cubic inch 4500 psi tank?

Of course we know that everytime you fill your pressure drops due to the volume of air excaping so lets say we don't want our 68ci tank to go below 1000 PSI and our SCUBA to go below 2000 PSI. also with air bleed of fill station will reduce the accuracy as well. I am just looking for something higher than a guess in which I can formulate other tank sizes and into this equation.

Thank you in advance to any positive input you may have in this.

[Redkey]

A> No... the both have the same amount of potential energy assuming both are actually 68cu-in tanks.

B> This has been discussed before... But I cannot find the articles. So...

the actual volume of a 80 cu-ft scuba tank is roughly 650 cu-in. So, I'll add 50% and call it a 120 cuft tank... 975 cu-in.

P1V1=P2V2
P1=pressure in scuba tank
V1=volume of scuba tank
P2=new pressure of the joined tanks
V2=volume of scuba tank and pressure tank linked together

3500 * 975 = (68 + 975) * P
P2=3272 <=new pressure in scuba tank and HPA tank.

now, if you use the HPA tank until the pressure drops to 1000 psi and then fill it from the same scuba tank the equation looks like this.

P1V1 + P2V2 = P3V3
P1=3272 = pressure in scuba tank
V1=975 = volume of scuba tank
P2=1000 = pressure in HPA tank
V2=68 = volume of HPA tank
P3=? = new pressure of system
V3=68+975 = volume of scuba and HPA joined together

(3272 * 975 + 1000 * 68 )/(68 + 975) = P3
P3=3124

you get the following sequence of values.

Scuba HPA HPA
Tank Start Final
3500 0 3272
3272 1000 3124
3124 1000 2985
2985 1000 2856
2856 1000 2735
2735 1000 2622
2622 1000 2516
2516 1000 2417
2417 1000 2325
2325 1000 2238
2238 1000 2158
2158 1000 2082
2082 1000 2012
2012 1000 1946

This is a quick conversion from a spreadsheet I had put together the first time this was asked. My original numbers were for a 80 cu-ft tank at 3,000 psi. You should double check my numbers since I have not.

[Mechanic79]

Pressure Chart

Thanks for the input, but I'm still confused on EXAMPLE A:

If you have a 68ci 4500PSI tank
when you have 4500 PSI filled in the tank you have 68 cu in of air.

If you have a 68ci 3000PSI tank
when you have 3000 PSI filled in the tank you have 68 ci of air.

So if you fill your 68ci 4500PSI tank to only 3000PSI you wouldn't have 68 ci of air.

BELOW IS A CHART I CAME UP WITH!

Tank A: 4500PSI / 68 c.i. = 66.176 PSI per c.i. @ 3000 PSI has 45.333 c.i.
Tank B: 3000PSI / 68 c.i. = 44.118 PSI per c.i.
Tank C: 4500PSI / 88 c.i. = 51.136 PSI per c.i. @ 3000 PSI has 58.667 cu in.
Tank D: 3000PSI / 88 c.i. = 34.091 PSI per c.i.
Tank E: 3000PSI / 47 c.i. = 63.829 PSI per c.i.
Tank F: 3000PSI / 51 c.i. = 58.823 PSI per c.i.

Tank A has 15.111 c.i. per 1000 PSI = .01511 c.i. per 1 PSI
Tank B has 22.630 c.i. per 1000 PSI = .02263 c.i. per 1 PSI
Tank C has 19.555 c.i. per 1000 PSI = .01955 c.i. per 1 PSI
Tank D has 29.333 c.i. per 1000 PSI = .02933 c.i. per 1 PSI
Tank E has 15.666 c.i. per 1000 PSI = .01566 c.i. per 1 PSI
Tank F has 17.000 c.i. per 1000 PSI = .01700 c.i. per 1 PSI

My 120 Cubic Foot Tank
120 c.f. x 1728 c.i. = 207360 c.i. @ 3500 PSI
3500PSI / 207360 = .01688 PSI per 1 c.i.
Tank has 59,241.706 c.i. per 1000 PSI
59.242 c.i. per 1 PSI


I remove 45.333 cu in of air from a full 3500PSI 207360 cu in tank.
207360 - 45.333 = 207314.667 cu in x .01688 PSI = 3499.5 PSI left in the tank.
Minus whatever is wasted from the Fill Station when bled.
120 tank @ 3000 PSI = 177,726 c.i. - 45.333 = 177,680.667 c.i. x .01688 = 2999.25 PSI left

Automag RT PRO
I get about 333 shots per 1000 PSI from my 68 c.i. 4500 PSI tankabout 1100 shots per 4500PSI fill.

This is what I have come up with not that it is correct or accurate in anyway I don't have the knowledge to test it but it may get some other thought provoketion.

[trains are bad]

So if you fill your 68ci 4500PSI tank to only 3000PSI you wouldn't have 68 ci of air.

No, wrong, you're way off base here. 68 cu inches of air is 68 ci of air. We're not talking moles here.

[Redkey]

You need to go a step further in your calculation and measure the amount of energy stored in the tank.

68 cuin @ 4500 psi = 306000 in-lbs of energy
68 cuin @ 3000 psi = 204000 in-lbs of energy

the units cancel out...
in * in * in * lb / in / in = in-lb

in your method you get
lb / in /in /in /in /in = lb/in^5
which are meaningless units.

The math you are trying to do doesn't make any sense. The volumes of the tanks are the same... they are just pressurized to different levels. 68 cu-in is 68 cu-in no matter what the pressure is.

Also, you didn't read my previous post very closely. Your 120 cu ft tank does not have a volume of 120 cu-ft. Think about it, 120 cu-ft is a box 1 ft x 1 ft x 120 feet long. The 120 cuft rating is the amount of uncompressed air it will hold. Measure the diameter and length of your tank, subtract 3/4" from both dimensions and then calculate the approximate volume. pi * radius* radius * length will give you the volume. If you redo your math (or mine) you'll see that the pressure drop on filling a 68 off your 120 is more than 0.5 psi.

[Cristobal]

Edit -- I see that Redkey posted again while I was typing this. Oh well, now you get two explanations!

PSI = Pounds (Force) / square inch (Area)

A gas under pressure exerts force on everthing around it -- the other gas molecules and ultimately the walls of the confining chamber, in this case the inner wall of your tank. But this force isn't applied at a single point to the surroundings, but an (essentially) equal force is applied to every single point over the entire area which encloses the gas. Hence, we talk about the force the gas exerts as a Force per Area -- it wouldn't make sense to talk about Force alone. If you cut your tank open and rolled it out and measured the area of the inner skin, you could multiply this by the 4500 PSI and find out the total Force that the gas applies to the inside of the tank when full.

It makes no sense to talk about PSI/ci ([Force/Area]/Volume) because every bit of gas inside the tank is essentially (to a very good approximation) at the same pressure and exerts the same force against everthing around it.

What you really want to talk about is ENERGY. If we make a reasonable approximation and treat the HPA as an ideal gas we can say that the energy contained in the gas is equal to its Pressure times its Volume -- thats the PxV that Redkey was talking about. As long as we don't let gas escape we know its Energy will be conserved, so if we change the volume by hooking up a small empty tank to the large full tank we can find the new pressure just as Redkey described.

When you compare PSI/ci for the 3000psi and 4500psi tanks, what I think you're trying to compar is Energy storage/ci for the two tanks. Given that E = P x V and the two volumes are identical, its pretty clear that higher pressure tank will store more energy. So if you wanted to you could figure out how much energy was stored per cubic inch for the 4.5k tank as opposed to the 3k tank. Of course if you express your energy in inches and pounds, and divide by 68 ci, you'll end up right back at 4500 pounds/square-inch!

[Mechanic79]

Thank you

Thank you, everyone, for your explanations. I understand it now. (for the most part at least)

No matter how much pressure, their is still the same cubic inch of air/space.

Now what if you pull a vacuum in the tank? J/K I'm not even going there :-)

I do appreciate everyones feedback

Mechanic79

[Cristobal]

Re: Thank you

Originally posted by Mechanic79
Now what if you pull a vacuum in the tank? J/K I'm not even going there :-)

If you pull a vacuum, all you've done is sucked all (perfect vacuum) of the air particles out. You have the same volume -- just nothing in it so there's no presure.

[athomas]

For 120 cubic foot tank at 3500psi

Scuba tank size = 120.0 cubic foot
actual tank size = 870.9 ci
tank rated psi = 3500.0 psi

air bottle = 68.0 cubic inches
starting pressure = 0.0 psi
residual pressure = 1000.0 psi before next fill

Stating pressure = 3500.0 psi
1st fill = 3246.5 psi
2nd fill = 3083.8 psi
3rd fill = 2932.9 psi
4th fill = 2792.9 psi
5th fill = 2663.1 psi
6th fill = 2542.6 psi
7th fill = 2430.9 psi
8th fill = 2327.3 psi
9th fill = 2231.1 psi
10th fill = 2142.0 psi
11th fill = 2059.3 psi
12th fill = 1982.5 psi
13th fill = 1911.4 psi
14th fill = 1845.4 psi
15th fill = 1784.2 psi
16th fill = 1727.4 psi

Hopefully my calculations are correct.

[athomas]

For 80 cubic foot tank at 3000 psi

Scuba tank size 80 = cubic foot
actual tank size = 677 cubic inches
tank rated psi = 3000 psi

air bottle = 68 cubic inches
starting pressure = 0 psi
residual pressure = 1000 psi

Stating pressure = 3000 psi
1st fill = 2726 psi
2nd fill = 2569 psi
3rd fill = 2426 psi
4th fill = 2296 psi
5th fill = 2177 psi
6th fill = 2070 psi
7th fill = 1972 psi
8th fill = 1884 psi
9th fill = 1803 psi
10th fill = 1730 psi
11th fill = 1663 psi
12th fill = 1603 psi
13th fill = 1548 psi
14th fill = 1498 psi
15th fill = 1452 psi
16th fill = 1411 psi

[the electrician]

a 68/3000 ci tank holds 8 cu ft of air at the 3000 psi
a 68/4500 ci tank holds 11 cu ft of air at the 4500 psi
a 45/4500 ci tank holds 7 cu ft of air at the 4500 psi

I know that much for sure.

[Mechanic79]

Three stage Manual pump

The FX three stage Manual pump 3000 PSI. Made in Sweden.
http://www.pyramydair.com/cgi-bin/ac...ccessory_id=81

or Three Stage Logan Pump 3000 PSI
http://www.pyramydair.com/cgi-bin/ac...cessory_id=458

Ok I got a spec that the Logan pump can pump 230cc per 1 stroke.

Is this math correct? 230 cubic centimeter = 14.0354611 cubic inch

If I'm able to pump 14.0354611 ci per every stroke is it possible to fill a 68ci tank to 3000 psi in just under 5 strokes?
68 / 14.0354611 = 4.844871110077

Thanks again everyone

[Thordic]

68 ci is the volume under pressure.

68 ci of air at 3000 psi is roughly 13,877 ci of air at STP, while 68 ci of air at 4500 psi is 20,816 ci.

The volume of a gas changes depending on pressure. Your air flow with that pump would be in atmospheric pressure.

You'd need to fill the above numbers to fill a tank. So if you could fill 14 ci per pump, it'd take almost 1000 pumps to get your tank full.