Calling all math nerds: Calculating volume dispensed by pressure?

For simplicity sake, lets say you have a 1 gallon corny. You fill it with 100 ounces of liquid. 28 ounces of headspace.

How much pressure would you need to dispense all 100 ounces?

Let's make it easy and assume the gas will not dissolve into the liquid and the liquid is flat.

I will assume the dip tube to tap is 1-foot. Pressure equivalent to 12-inches of water head (~0.4-0.5 psi) is required to get the last bit out. If tap is higher, take that pressure and multiply by the number of feet from dip tube to tap.

What are you after with this question?

Not enough/incorrect data.

You're not accounting for the siphon effect. Simple answer, as long as the relative pressure at the outflow is less than at the inlet, you will empty the bucket.

we won't even address the issue of "28 ounces of headspace"

It's not pressure that you would measure, but mass that you would need to measure in this case. You would need to declare the pressure you are serving at then, let's say 13 psi. Then you can calculate the density of the CO2 using a lookup table, or in my case, a software package. In my analysis, I am ignoring the dissolved CO2 like you requested, as well as the CO2 in the lines, as this can vary a bit, but this should give you a general idea magnitudes.

My work is shown in the attached pictures. You will use up about 0.03 lbm of CO2 for each one gallon keg. One important thing to note, however, is that to fully dispense all of the keg at this pressure, you will need to have enough CO2 left in the canister to maintain at least your 13 psi serving pressure. I don't have any information on the volume of 5 lbm or 10lbm tanks, so I can't help you with that part, but perhaps someone else can, or if you have a tank that has that information labeled on it, I can add that to this analysis.

If anyone else sees an error in my calculations, please let me know, but I'm pretty sure this is fairly accurate.

Rhumbline said:

Not enough/incorrect data.

You're not accounting for the siphon effect. Simple answer, as long as the relative pressure at the outflow is less than at the inlet, you will empty the bucket.

we won't even address the issue of "28 ounces of headspace"

Click to expand...

For the siphon situation, all you would need to know is the starting delta between the liquid surface and the highest point in the serving line. If that is one-foot, you need around 0.5 psi to push the beer to the high-point and start the siphon. Headspace doesn't matter for his specific question (pressure, not mass/volume).

wardens355 said:

For the siphon situation, all you would need to know is the starting delta between the liquid surface and the highest point in the serving line. If that is one-foot, you need around 0.5 psi to push the beer to the high-point and start the siphon. Headspace doesn't matter for his specific question (pressure, not mass/volume).

Click to expand...

That, and the post above it, is a much more comprehensive answer than what I offered.

Excellent analysis Jakor. That definitely helps me work through this.

Here's what I'm after with this question.

If I wanted to dispense a 1 gallon Cornelius keg, how much gas would I need initially to remove all the liquid? Let's say I want to bring water in a corny keg, but don't want to bring a gas tank to dispense it. Just a tap mounted to the liquid out and a charge of nitrogen (much less soluble than c02) before I left.

I gave the 100 ounce liquid/28 ounces of headspace as a gross oversimplification of the scenario I was working with. By trying to make this simple I left out a lot of information! I'm not after accuracy just simply approximation.

It's only a hundred ounces. Remove it from the fridge, pop the top and just pour it directly into your mouth.

Are you suggesting that the headspace would be charged one time prior to dispensing the full container and asking what the pressure needs to be to not run out of gas before it's empty?

Bobby_M said:

Are you suggesting that the headspace would be charged one time prior to dispensing the full container and asking what the pressure needs to be to not run out of gas before it's empty?

Click to expand...

Yes, exactly.

Volume and pressure are linearly inversely proportional. Start with the minimum ending pressure. You can probably get away with 1-2 psi at the last drop. Now consider the ratio of headspace to total container volume. If you have 9/10th liquid and 1/10th headspace then 10 psi in the headspace will drop to 1 psi when empty. 20 will get down to 2 psi.

Very interesting question, but it seems that this would allow you to serve in a very low profile way.

Based on how cryptic the original post was, wh I knows what is being dispensed

Word, @Bobby_M . Thanks for posting all the science!
It seems slightly insane to try to pressurize your keg to have enough to push out the last ounces... I mean, if you figure that a full 5 gallon corny has, what, 1/20 of its volume as airspace, then you're figuring you need 240psi (!!!) to have 12 psi for the last 20th of the keg? Sounds like a bomb to me... Even at 1/10 airspace that's still 120psi. Nice thought exercise, but not really practical irl.