Compressed Nitrogen: Calculating Pipe Flow Time

[Nicholas Hankins]

Hello, first time on this site and wondered if anyone could help me on what the proper equation or equations would be to answer this question.

I have a 300 cubic foot tank of nitrogen air that will provide nitrogen to a rectangular pipe at 5 psi with a flow rate of 10 CFM to atmosphere at the end of the rectangular pipe. The question is how long would it take the 300 cubic foot tank to empty?

 

[berkeman]

Hello, first time on this site and wondered if anyone could help me on what the proper equation or equations would be to answer this question.

I have a 300 cubic foot tank of nitrogen air that will provide nitrogen to a rectangular pipe at 5 psi with a flow rate of 10 CFM to atmosphere at the end of the rectangular pipe. The question is how long would it take the 300 cubic foot tank to empty?

Welcome to the PF.

I think we need the starting pressure in the tank as well. It is regulated down to 5psi for the flow, right?

Also, this sounds a bit like a schoolwork question, but I'm guessing it is for your work?

 

[Nicholas Hankins]

Yes it is for work. And also yes it will be regulated down to 5 psi for the flow. The Tank will actually hold 341 Cubic feet at 3500 psi.

 

[berkeman]

Yes it is for work. And also yes it will be regulated down to 5 psi for the flow. The Tank will actually hold 341 Cubic feet at 3500 psi.

It seems like you could get an initial estimate just using the Ideal Gas Law. Are you familiar with that equation?

http://hyperphysics.phy-astr.gsu.edu/hbase/Kinetic/idegas.html

 

[Nicholas Hankins]

Yes I am. I don't know if I am looking at this problem the right way though.

 

[Nicholas Hankins]

I am not sure how to get an estimate with that equation with respect to time?

 

[berkeman]

I am not sure how to get an estimate with that equation with respect to time?

You have an outflow rate at 5psi and an initial stored volume of gas...

 

[Nicholas Hankins]

okay. the initial time it would take from my calculation with a 341 cf tank at 10 cfm is 34.1 minutes. Am I correct though that the pressure drop in the regulator and the length and area of the piping change the depletion rate of the tank as well?

 

[Chestermiller]

What is the mass in the tank to begin with? What is the mass flow rate out?

 

[Nicholas Hankins]

from what I have calculated it is 10.63 Kg in the tank with a mass flow rate out of the rectangular pipe is 3.55 Kg/m

 

[Chestermiller]

from what I have calculated it is 10.63 Kg in the tank with a mass flow rate out of the rectangular pipe is 3.55 Kg/m

So, from this, it seems that, if the flow rate did not decrease as the tank emptied, it would take about 3 minutes to empty the tank. Is that a good enough answer for you?

 

[Chestermiller]

from what I have calculated it is 10.63 Kg in the tank with a mass flow rate out of the rectangular pipe is 3.55 Kg/m

That 10.63 kg can't be right. I get about 2600 kg. I haven't checked your discharge rate yet, but maybe that's wrong too.

 

[Chestermiller]

I get a discharge rate of 15.7 kg/m. Based on an initial mass of 2600 kg, it would give a (very rough) emptying time on the order of about 3 hours.

 

[Nicholas Hankins]

yes it does thank you. I thing using liquid nitrogen would be better for this use.

 

[Nicholas Hankins]

how did you get your 2600 kg?

 

[Chestermiller]

how did you get your 2600 kg?

I used the ideal gas law, with a pressure of 3500 psi.

 

[Nicholas Hankins]

Oh Okay. Thank you very much for your help.