Compressed Nitrogen: Calculating Pipe Flow Time

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Discussion Overview

The discussion revolves around calculating the time it would take for a 300 cubic foot tank of nitrogen to empty when supplying gas through a rectangular pipe at a regulated pressure of 5 psi and a flow rate of 10 CFM. Participants explore various equations and concepts, including the Ideal Gas Law, to estimate the depletion time, while addressing factors such as pressure drop and mass flow rate.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant asks for the proper equations to determine how long it would take to empty the tank.
  • Another participant notes the importance of knowing the starting pressure in the tank, which is regulated to 5 psi.
  • It is mentioned that the tank holds 341 cubic feet at 3500 psi, and one participant suggests using the Ideal Gas Law for an initial estimate.
  • One participant calculates an initial time of 34.1 minutes based on a flow rate of 10 CFM but questions the impact of pressure drop and pipe dimensions on the depletion rate.
  • Participants discuss the mass in the tank and the mass flow rate out, with one participant calculating 10.63 kg in the tank and a mass flow rate of 3.55 kg/m.
  • Another participant challenges the initial mass calculation, suggesting it should be around 2600 kg, leading to a different estimate of emptying time.
  • Discharge rates are also debated, with one participant calculating a rate of 15.7 kg/m based on the revised mass.
  • One participant suggests that using liquid nitrogen might be a better option for the application.

Areas of Agreement / Disagreement

Participants express differing views on the initial mass of nitrogen in the tank and the corresponding calculations for emptying time. There is no consensus on the correct values or methods to use, and multiple competing estimates are presented.

Contextual Notes

Participants rely on the Ideal Gas Law and other assumptions, but there are unresolved questions regarding the accuracy of mass flow rates and the effects of pressure changes during the tank's depletion.

Nicholas Hankins
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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?
 
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Nicholas Hankins said:
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. :smile:

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?
 
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.
 
Nicholas Hankins said:
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
 
Yes I am. I don't know if I am looking at this problem the right way though.
 
I am not sure how to get an estimate with that equation with respect to time?
 
Nicholas Hankins said:
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...
 
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?
 
What is the mass in the tank to begin with? What is the mass flow rate out?
 
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  • #10
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
 
  • #11
Nicholas Hankins said:
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?
 
  • #12
Nicholas Hankins said:
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.
 
  • #13
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.
 
  • #14
yes it does thank you. I thing using liquid nitrogen would be better for this use.
 
  • #15
how did you get your 2600 kg?
 
  • #16
Nicholas Hankins said:
how did you get your 2600 kg?
I used the ideal gas law, with a pressure of 3500 psi.
 
  • #17
Oh Okay. Thank you very much for your help.
 

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