Gas conductance through tube at low pressure

In summary, the conversation discusses the design of a vacuum chamber with a controllable tube to achieve a constant rate of pressure change inside the chamber. The use of PV=nRT and Poiseuille's law for calculating the required tube radius is questioned, and a different equation is suggested for the low pressure regime. It is determined that a control system with a pressure sensor and flow control valve will be necessary for this setup.
  • #1
soothsayer
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I have a vacuum chamber of volume V connected to a vacuum pump via a tube of radius R and length L, and I want to design this "tube" such that R can be controlled in order to provide a constant rate of pressure change inside of the chamber of 2.5 mbar/sec, from atmosphere down to ~0.5mbar. Assume that pumping speed is infinite, so my flow rate is entirely limited by the conductance of my adjustable tube.

At the beginning of chamber pumpdown, I feel like I should be able to apply a combination of PV=nRT and Poiseuille's law to convert my 2.5mbar rate of pressure change into a desired flow rate, and then into an effective tube radius. When I do this, I get a result that feels pretty intuitive based on my experience. (Does this seem like a valid calculation to anyone else or have I already made an error here?)

But nearing the end of the pumpdown process, I suspect I can no longer apply Poiseuille's law in the same way since I no longer have laminar gas flow. When I try to apply the same equations the same way I get a resulting effective radius that is much smaller than would make sense. Is there a different equation I can use to calculate a required tube radius in this low pressure regime? Does it even make sense to be trying to calculate this when my desired change in pressure (2.5mbar/s) is larger than my chamber pressure (0.5mbar)? It doesn't feel like I can treat pressure over time as linear here.

Any advice for tackling this problem would be appreciated!
 
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  • #2
This sketch is my understanding of your problem:
Vacuum.jpg

The Poiseuille equation applies to the incompressible laminar flow of a Newtonian fluid. Air is Newtonian, the Reynolds number needs to calculated to find if the flow is laminar, and this flow is definitely not incompressible.

Your goal is to get a constant rate of pressure decrease in the vacuum chamber. That requires a constant mass flow rate out of the chamber. At the start, the pressure (and the density) in the chamber is high, and the pressure drop is high. Near the end, the pressure (and the density) in the chamber is low, and the pressure drop is low. Regardless of whether the flow in the tube is laminar or turbulent, the mass flow rate will be a function of chamber gas density and pressure drop in the tube. The mass flow rate will be high at the beginning, and decrease as the pressure in the vacuum chamber decreases.

A fixed restriction, whether a tube or an orifice, will not get you a constant rate of pressure decrease in the vacuum chamber. Unless somebody has a better idea, I think you will need some sort of control system. A pressure transmitter, ramp controller, and air flow control valve would do what you want.
 
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Likes DaveE
  • #3
soothsayer said:
I have a vacuum chamber of volume V connected to a vacuum pump via a tube of radius R and length L, and I want to design this "tube" such that R can be controlled in order to provide a constant rate of pressure change inside of the chamber of 2.5 mbar/sec, from atmosphere down to ~0.5mbar. Assume that pumping speed is infinite, so my flow rate is entirely limited by the conductance of my adjustable tube.

At the beginning of chamber pumpdown, I feel like I should be able to apply a combination of PV=nRT and Poiseuille's law to convert my 2.5mbar rate of pressure change into a desired flow rate, and then into an effective tube radius. When I do this, I get a result that feels pretty intuitive based on my experience. (Does this seem like a valid calculation to anyone else or have I already made an error here?)

But nearing the end of the pumpdown process, I suspect I can no longer apply Poiseuille's law in the same way since I no longer have laminar gas flow. When I try to apply the same equations the same way I get a resulting effective radius that is much smaller than would make sense. Is there a different equation I can use to calculate a required tube radius in this low pressure regime? Does it even make sense to be trying to calculate this when my desired change in pressure (2.5mbar/s) is larger than my chamber pressure (0.5mbar)? It doesn't feel like I can treat pressure over time as linear here.

Any advice for tackling this problem would be appreciated!
Hi There!

This is a super fun problem. Are you still looking for help?

Check out the PDF by Genick Bar-Meir, "Fundamentals of Compressible Fluid Mechanics"

Let me know if you need help.
 
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  • #4
jrmichler said:
I think you will need some sort of control system. A pressure transmitter, ramp controller, and air flow control valve would do what you want.
Yep. This!
You will absolutely have to have a some flow control "valve" that can be adjusted. You will also need a pressure sensor to measure what you ultimately want. The rest is just a (nonlinear) control system to make it work.
 

FAQ: Gas conductance through tube at low pressure

1. What is gas conductance?

Gas conductance refers to the ability of a gas to flow through a tube or channel at a certain pressure. It is a measure of the ease with which a gas can move through a given space.

2. What is considered low pressure for gas conductance?

Low pressure for gas conductance is typically defined as pressures below 1 Torr (1 mmHg). At this pressure, the mean free path of the gas molecules is much larger than the dimensions of the tube, allowing for free molecular flow.

3. How does the diameter of the tube affect gas conductance at low pressure?

The diameter of the tube has a significant impact on gas conductance at low pressure. As the diameter decreases, the mean free path of the gas molecules increases, resulting in a decrease in gas conductance. This is due to a higher likelihood of gas molecules colliding with the walls of the tube.

4. What factors influence gas conductance through a tube at low pressure?

Several factors can influence gas conductance through a tube at low pressure. These include the diameter and length of the tube, the type of gas being used, the temperature of the gas, and the surface characteristics of the tube walls.

5. How is gas conductance measured at low pressure?

Gas conductance at low pressure can be measured using various techniques, such as the pressure rise method or the throughput method. These methods involve measuring the pressure difference between two points in the tube and calculating the gas flow rate using the ideal gas law.

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