Air flow from atmosphere into a tank

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Discussion Overview

The discussion revolves around determining the flow rate of air entering a depressurized tank at 0.2 bar absolute pressure. Participants explore the relationship between flow rate and pressure, considering factors such as conductance, viscous flow, and the implications of switching the vacuum pump on or off.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant seeks an equation to determine the flow rate into the tank over time, noting the interdependence of flow rate and tank pressure.
  • Another participant suggests that the flow rate is determined by the conductance of the pipe and mentions the use of equations for viscous flow, assuming laminar conditions at the given pressures.
  • A reference to the ideal gas law is made, indicating that it can relate flow rate to the time derivative of pressure, leading to a first-order differential equation.
  • Questions arise about whether conductance applies only when the vacuum pump is operational, with a participant clarifying that conductance is relevant for any pressure difference, regardless of the pump's status.
  • It is noted that without the pump, the low-pressure side will change over time according to the flow rate dictated by conductance, requiring integration over time, which results in a simple exponential function.
  • Participants discuss the distinction between molecular flow and viscous flow, asserting that the type of flow depends on pressure rather than the state of the pump.

Areas of Agreement / Disagreement

Participants express differing views on the applicability of conductance and the nature of flow (molecular vs. viscous) under various conditions. The discussion remains unresolved regarding the specifics of flow rate equations and the implications of switching the vacuum pump on or off.

Contextual Notes

Participants reference the need to integrate over time when considering flow rates and pressure changes, but the exact mathematical steps and assumptions involved are not fully detailed.

JCB123
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Hi,
I have a tank of air which has been depressurized to 0.2bar (absolute) via a vacuum pump, where air can be let in from atmosphere through pipework controlled by a valve. What would be the equation I can use to determine the flow rate into the tank with time? As the flow rate is determined by the pressure inside the tank, and the pressure inside the tank is determined by the flow rate.
Thanks
 
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At any moment you will have a flow rate determined by the conductance of the pipe. You can read about that here:

https://www.pfeiffer-vacuum.com/en/...o-vacuum-technology/fundamentals/conductance/

At your pressures the mean free path is always smaller than the dimensions of the vessels, so you will use the equations for viscous flow and you will probably also want to assume the flow is laminar.

So that will give you flow rate as a function of pressure. However the flow rate can be related to the time derivative of pressure by the ideal gas law, so this will give you a first order differential equation in pressure which you can easily solve (you'll get a simple exponential)
 
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JCB123 said:
Hi,
I have a tank of air which has been depressurized to 0.2bar (absolute) via a vacuum pump, where air can be let in from atmosphere through pipework controlled by a valve. What would be the equation I can use to determine the flow rate into the tank with time? As the flow rate is determined by the pressure inside the tank, and the pressure inside the tank is determined by the flow rate.
Thanks

Another good reference is "Building Scientific Apparatus" by John Moore which in addition to pumping also discusses just about everything of practical interest to the experimental physicist. I highly recommend it.
 
Thanks!
Does conductance only apply when the vacuum pump is switched on? If I switch off the pump and just open the valve to let the flow in, is it the equations for viscous flow I need to use?
 
JCB123 said:
Thanks!
Does conductance only apply when the vacuum pump is switched on? If I switch off the pump and just open the valve to let the flow in, is it the equations for viscous flow I need to use?

The conductance applies for a difference in pressure regardless of how that is achieved. The difference between pump on and pump off is that without pumping the low pressure side will change pressure over time according to the flow rate dictated by the conductance. You therefore have to integrate over time. This integrates easily to a simple exponential.

Molecular flow vs viscous flow does not depend on pump on or pump off. It only depends on the pressure. At your pressures you will only ever use viscous flow.
 
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