What is the Relationship Between Pressure and Time in a Leaking Container?

[durkamurka]

Hi,

I'm trying to figure out how i can mathematically represent the pressure inside of a container that is being pumped with air, and slowly leaking air.

The pressure inside the container would increase and decrease over time as more air is pumped in and is leaked out. The pressure would have to be represented in a nonlinear way.

The problem is there are a lot of factors that affect the pressure inside the container and I can't figure out where to start.

 

[Dr.D]

The ideal gas law is a good place to start, and then supplement this with some models for the mass flow in and the mass flow out.

 

[Andy Resnick]

Why does the pressure have to be 'represented in a nonlinear way'? Say the container is perfectly rigid; you have a mass flow in and out at constant volume (and temperature); use the ideal gas law PV=nRT to get the pressure. If you wish to make the problem more complex you may of course do so.

If the container is not rigid, then I agree the problem may become nonlinear becasue you have to couple the pressure and the membrane tension, and the volume is not constant.

 

[Dr.D]

I suspect that the original questioner is thinking of pressure as a driving function. In point of fact, the mass flow rates are the driving functions, and pressure depends on volume, temperature, and mass in the vessel. No reasonable person uses a balloon for a pressure vessel.

 

[durkamurka]

thanks for the responses this helps a lot.

The question is referring to the pressure inside of the plenum(air) chamber of a hovercraft.

In this situation, a fan is blowing air into the plenum at a certain rate, and air is escaping through the bottom of the craft through slots (speed of the air depending on the size of the slots), filling a bag skirt and creating lift via a thin film of air leaving underneath the bag. the plenum itself is airtight.

I have been referring to https://www.physicsforums.com/showthread.php?p=2128543" post and think i can work with it.

 

[Andy Resnick]

I suspect that the original questioner is thinking of pressure as a driving function. In point of fact, the mass flow rates are the driving functions, and pressure depends on volume, temperature, and mass in the vessel. No reasonable person uses a balloon for a pressure vessel.

I hear you, but be careful: balloons can make excellent constant-flow reserviors:

http://www.hrmedical.com/catalog/category/Homepump-C-Series-for-Chemotherapy.html
http://www.medscape.com/viewarticle/537694_3

We also looked at inflatable tanks for constant-flow delivery of water in spacecraft applications.