# Gas flow, time required to fill a tank

1. Jun 18, 2012

### jnesbit

Hi all,

I've been searching through the forum, and found some related posts, but still can't wrap my head around this. I would greatly appreciate any help.

I'm trying to fill a box with carbon dioxide from a tank, that has attached to it a regulator and tube.

I used PV = nRT to find the volume of CO2 inside the tank; here are all my variables:
P (inside tank) = 4601.325 kPa
V (inside tank) = 0.273 cubic meters
n = 515.32 moles
R = 0.0083 (m3*kPa/mol*K)
T = 293 K

I want to know how long it would take to fill a box with CO2 from this tank. The regulator on the tank shows the pressure inside the tank is 4,500 kPa and the pressure of CO2 exiting the tank is 40 kPa. The diameter of the tube through which CO2 exits the tank is 1/8 inch.

I've taken 3 non-calculus-based physics classes, and passed thanks to some hideous curve. So I'm trying to escape this dumbed-down understanding my university has so graciously given to me...

Thank you!
Nathan

2. Jun 18, 2012

### haruspex

I've no idea whether this is right, but I tried this:
Treat the 40kPa acting over the area of the pipe as a force accelerating the gas up to its flow speed. By conservation of energy, the linear speed that results is √(2P/ρ) where P is the pressure and ρ the density. For a volumetric rate that's A√(2P/ρ). Question is, what pressure and density? Using the 40kPa and ρ = 2kg/m3, it gives 1.6 litres/s. Using the 4500 kPa gives 10 times that.
This assumes the pipe is very short. For a longer pipe you have to take into account the pressure gradient along it.

3. Jun 18, 2012

### nasu

"Filling a box" with gas is not meaningful unless you specify the desired pressure of the gas in the box. Otherwise, any amount of gas, no matter how much, will expand to "fill the box" in the sense that it will occupy the entire volume of it.

4. Jun 19, 2012

### jnesbit

The desired pressure of the gas in the box... good point. I guess I thought even though a gas would fill the box, there would still be a "normal" density/volume it would occupy. Sort of like a saturation point, where it wouldn't be building pressure, and it wouldn't be "loose."

My problem might be more of a conceptual one; there is no lid to the box. I'm just basically lowering the CO2 tube into the box, letting it run for a few minutes, and then removing it. I'm hoping that the stagnant air in the room, plus the density of CO2 being greater than air, will at least somewhat contain the CO2 in the box.

If this is something that would require a doctorate in physics, like to understand the movement of air particles and "how much is enough" in order to keep a reasonable amount of CO2 in the tank while allowing for a minimum amount to spill out, so as to waste as little CO2 as possible... I can just keep doing what I've been doing, which is run the CO2 for 2-4 minutes and hope for the best.

5. Jun 19, 2012

### nasu

OK, I thought you may want to do something like this.
As you say, this is not a stable state. Some CO2 will leak out in time.
However you can estimate how much CO2 you need to replace the air in the box (initially full with air).
The volume of the CO2 is the volume of the box. You need to measure this, you cannot calculate it from the gas law.
Then you can take the pressure equal to atmospheric pressure and temperature equal to the room temperature at location.
Then from the gas law you can fin how many moles of CO2 in normal conditions will fit in the box. You can also find the mass of CO2 if you multiply number of moles by molecular mass (44 g/mole for CO2).
To find the time you will need to know the flow rate of your source (either volume, mass, molar).