When is 500 psi not 500 psi?

[rsterne]

I have been shooting my .257 Monocoque tethered at 3800 psi the past few days, and I can't seem to get the efficiency that I want.... I know that between 3000 psi and 4500 you can't cram as much air into the tank as Boyle's Law says you should be able to.... (which is why a 550 CI - 60 min SCBA tank is 88 CF, not 97 CF).... so I did a few quick calculations and you might find the results interesting.... For each 500 psi pressure drop, I calculated the decrease in the density of the air over that 500 psi, and then divided by the density at 1 Atm.... The results below are the number of CF of air at 1 atmosphere that the tank discharged during that 500 psi pressure drop....

1500 psi down to 1000 psi.... 10.9 CF (Boyle's Law predicts 10.8 CF)
3000 psi down to 2500 psi.... 9.5 CF (12% less than Boyle predicts)
4500 psi down to 4000 psi.... 7.5 CF (31% less than Boyle predicts)

What does this mean if I am calculating the efficiency in FPE/CI when my tank is dropping from 4500 psi down to my regulator's 3800 setpoint?.... Well, compared to what we usually do, using Boyle's Law, I am actually only getting 72% as much air at 3800 psi as I thought I was when my tank drops from 4500 to 3800.... so basically every 3 shots I took caused the pressure in my Great White to drop like I just took a little over 4 shots....  .... That means if I thought I was getting 0.75 FPE/CI, I was actually getting 1.04 FPE/CI.... Hey, at over 200 FPE with a .257 cal, I can certainly live with that.... 

Now you know why your 4500 psi tank seems to lose pressure more quickly, ie over fewer shots, when it is full, than is does once it gets down to 3000 psi or less.... You can blame a guy by the name of VanDerWaals for figuring it out....  .... I'm just the messenger.... 

Bob

[anti-squirrel]

Falls in line with my own experiences recharging HVAC systems- not the actual recharging, but when leak-testing using nitrogen. 

Also saw interesting things on the sub falling in line with that especially after PMs and servicing.  And once you factor in temperature differentials, we always ended up running our HP air compressors more frequently than the plain math would dictate. 

Thanks for the refresher- it's one of those things I stopped paying attention to and shouldn't have.


EDIT: we had to plot out stuff like this in Nuke School, then calculate the variance over time.  I can't recall exactly, but it resembled a parabola with a gutter, and it uses Avogadro's Number (technically a constant) and some other fancy things- in particular the actual mass, not weight.   Heat transfer plays a role, too.  Maxwell, Boyle, Avogadro, Boltzman... all those guys I've done my darnedest to forget.   Now I'm not going to be able to sleep in this hotel room- all I'll be thinking about is how much better van der Wall's equation is over the Ideal Gas Law.  And how much more it made my life stink back then.

[rsterne]

It certainly is an argument for the declining returns of using ever increasing pressures for airguns.... as that trend continues at even higher pressures.... Dropping from 6000 psi to 5500 releases only HALF the expected amount of air, at just 5.4 CF.... 

Bob

[Sfttailrdr46]

It certainly is an argument for the declining returns of using ever increasing pressures for airguns.... as that trend continues at even higher pressures.... Dropping from 6000 psi to 5500 releases only HALF the expected amount of air, at just 5.4 CF.... 

Bob

You just enjoy making my head hurt Bob. I am beginning to think that somewhere inside that cute furry purple body lurks the soul of a sadist that loves to think up new ways to torture those of us who know just enough math to sort of get the gist of what you are saying but not without some additional home work. 

[45Bravo]

I guess that means Boyles law, isn't a really law.

It's now more of just a guideline...

[rsterne]

Boyle's Law is for ""Ideal Gasses".... Unfortunately, at high pressure, they no longer act as ideal.... Here's a good one for you.... Using Boyle's Law, if you had one 88 CF SCBA tank filled to 4500 psi and another empty (14.7 psi), both at 20*C, and connected them together, opened a valve and let the pressure equalize and then the temperature stabilize back to 20*C, what would the pressure be?.... The classical answer is (4500 + 14.7) / 2 = 2257 psi.... Anyone want the correct answer?.... Too late to decline, I'll post it in the next post....

Bob

[rsterne]

The answer is 2028 psi, over 10% lower than Boyle's Law would predict.... It is the exact same phenomenon that is responsible for that 88 CF SCBA tank (550 CI internal volume) only holding 88 CF at 4500 psi, whereas Boyle's Law would predict it would hold (550 x 4500 / 14.7 / 1728) = 97.4 CF.... and yes, that is why the Great White is advertised at that number, IMO.... To fill a 550 CI SCBA tank to 97 CF would raise the pressure to over 5000 psi....

Bob

[SpiralGroove]

For each 500 psi pressure drop, I calculated the decrease in the density of the air over that 500 psi, and then divided by the density at 1 Atm.... The results below are the number of CF of air at 1 atmosphere that the tank discharged during that 500 psi pressure drop....
1500 psi down to 1000 psi.... 10.9 CF (Boyle's Law predicts 10.8 CF)
3000 psi down to 2500 psi.... 9.5 CF (12% less than Boyle predicts)
4500 psi down to 4000 psi.... 7.5 CF (31% less than Boyle predicts)
What does this mean if I am calculating the efficiency in FPE/CI when my tank is dropping from 4500 psi down to my regulator's 3800 setpoint?.... Well, compared to what we usually do, using Boyle's Law, I am actually only getting 72% as much air at 3800 psi as I thought I was when my tank drops from 4500 to 3800.... so basically every 3 shots I took caused the pressure in my Great White to drop like I just took a little over 4 shots....  .... That means if I thought I was getting 0.75 FPE/CI, I was actually getting 1.04 FPE/CI.... Hey, at over 200 FPE with a .257 cal, I can certainly live with that.... 

Now you know why your 4500 psi tank seems to lose pressure more quickly, ie over fewer shots, when it is full, than is does once it gets down to 3000 psi or less.... You can blame a guy by the name of VanDerWaals for figuring it out....  .... I'm just the messenger....  ............ Bob

Hey Bob,
Is VanDerWaals formula accessible (enough) so that "Business" majors can reasonably calculate this variable, diminishing air flow rate at higher pressures?   Does Lloyd's calculator take this into effect?

[rsterne]

I don't even understand all the math, and it's different for every gas.... You can use the "Peacesoft" calculator to find the air density at whatever pressure you want, and then go from there....

http://www.peacesoftware.de/einigewerte/luft_e.html

For example, enter 310 bar (4500 psi) and 20*C (68*F) and you get an air density of 330.78 kg/m^3.... Put in 1 bar (14.5 psi) and you get 1.1894.... If you divide (330.78 / 1.1894) = 278.11 for the ratio of the densities.... instead of the 310 predicted by Boyle's Law.... What this is telling you, is that there are 278 times as many molecules in a given volume at 4500 psi, instead of 310.... basically the pressure is increasing faster than the density.... So, when you expand that 4500 psi air back to 1 bar, you end up with fewer molecules than Boyle says you should, so the volume (at 1 bar) would be less....

Sorry to cop out on you on the math, if the answer was easy I wouldn't be using an online calculator.... There is another set of calculators, by Wolfram, that can give you almost anything you need.... http://www.wolframalpha.com/input/?i=air+density+at+310+bar

Just type in your inquiry in the search box (eg. "air density at 310 bar") and it spits out all the info.... It "knows" a lot of cool stuff.... try typing in "speed of sound in air at 310 bar and 50C", and you'll see what I mean.... 

Lloyd's online calculators don't take into account VanDerWaals, I think it might be too complex to include (but I will ask him).... It might be significant in calculating the number of fills you can get on a 3000 psi rifle from a 4500 psi tank.... certainly using Boyle's predicts too high a number....

Bob

[SpiralGroove]

Thanks Bob ............ for the stuff on the margins
It keeps the GTA interesting .

[anti-squirrel]

IIRC, the whole reason each gas is impacted differently is van der Waal's equations looks at the molar mass (molar volume of the gas[es] in question)  Not the little rodents, mind you.  Blended gases (solutions) act even more differently- to get properly accurate results you have to know the exact ratio, and if you have isotopes of the gases, throw in another set of variables.  Dang it, another sleepless night.

The wiki article isn't too bad, but it takes a tangent and goes down the thermodynamics route, which is exactly what we were supposed to learn in Nuke School.  I say supposed to since I clearly did not learn, I memorized and have forgotten in the ensuing decades.  Still basic rule of "hotter gases expand despiite overall mass, thus volume increase as T increases"

Don- IIRC, you used to do HVAC work.  It's like leak-testing with nitrogen after a compressor replacement.  Expected drop from a higher pressure always results in a slightly greater pressure drop on the bottle than expected.

[Sfttailrdr46]

All to true and I taught HVAC for two years that was a challenge some of the students were HS dropouts with issues. So teaching electrical theory not to mention thermodynamics and flow rates through heat exchangers fugedaboudit 

[lloyd-ss]

My online fill calculator and efficiency calculator do not use VanDerWaals.  Heck, when I did those, I wasn't even aware of VanDerWaals, and 4500 psi, where this has more significance, was rare, and only for the rich.  Things have changed fast with PCPs, so maybe I should think about revisiting that.  However, getting my head wrapped around it needs to happen first.
Lloyd 

[45Bravo]

My guess would have been wrong, but not by much.
2250 was my guess.

As we say, it's close enough for government work..

Math was not my strong point.
And still isn't.

I live by the mantra, "and yet another day Dr. Malone was wrong, I didn't use algebra today."

This was my college professor that used to dream numbers and equations.
And told us we would use algebra everyday in our adult lives.

[rsterne]

Ian, you saw that the correct answer was 2028 psi, right?.... 10% less than your guess, and what Boyle's Law would predict.... Unfortunately, High School Physics lies a lot, but it keeps the concepts simple enough for 90% of everyday life.... plus or minus 10%, right?.... Most of the time, who cares.... 

Bob

[plinker81366]

bob, in a regulated set up, and we are estimating shot count thru interpolation,  does that mean we actually get lesser shot count, than the interpolated  shot count estimate?

[plinker81366]

maybe interpolated shot ct (.9) would be very near

[rsterne]

It depends on the supply pressure in the tank, and the regulator setpoint.... The big difference (enough to notice) takes place over 3000 psi.... so if you are filling to 3000 and your regulator is set at 1500 psi, you won't notice much of a loss in shot count.... maybe 6% at most, with most of that loss coming in the first 500 psi, from 3000 down to 2500.... If you then change to a 4500 psi tank, however, and expect to get twice the number of shots (because you have 3000 psi of "headroom" instead of 1500), you won't get that, because the pressure will drop faster from 4500 to 3000 than from 3000 to 1500, even though the amount of air being used for each shot (at 1500 psi) is exactly the same....

You will only get about 81% of the number of shots from 4500 psi down to 3000 that you will from 3000 down to 1500, in a gun regulated at 1500 psi.... ie 1.8 times as many, not double as you would expect.... To expand on this idea further, if you had a 6000 psi tank, regulated down to 1500 psi, you would expect to get 3 times as many shot as you would from 3000 down to 1500.... In fact, you would get only 2.4 times as many....

Bob

[oldpro]

We need Lloyd to put that in his spread sheet calculator

[plinker81366]

It depends on the supply pressure in the tank, and the regulator setpoint.... The big difference (enough to notice) takes place over 3000 psi.... so if you are filling to 3000 and your regulator is set at 1500 psi, you won't notice much of a loss in shot count.... maybe 6% at most, with most of that loss coming in the first 500 psi, from 3000 down to 2500.... If you then change to a 4500 psi tank, however, and expect to get twice the number of shots (because you have 3000 psi of "headroom" instead of 1500), you won't get that, because the pressure will drop faster from 4500 to 3000 than from 3000 to 1500, even though the amount of air being used for each shot (at 1500 psi) is exactly the same....

You will only get about 81% of the number of shots from 4500 psi down to 3000 that you will from 3000 down to 1500, in a gun regulated at 1500 psi.... ie 1.8 times as many, not double as you would expect....

Bob

thanks Bob, lol yup 3 kpsi fill