Air flow from atmosphere into a tank

[JCB123]

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

 

[Cutter Ketch]

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)

 

[Cutter Ketch]

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.

 

[JCB123]

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?

 

[Cutter Ketch]

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.