Fluid mechanics modeling question

[spiri]

Physics Forum:

Can someone show me how to model, mathematically, what happens if you place a drink box with a straw sticking out of it, in a vacuum chamber and apply a vacuum?

 

[Chestermiller]

Are you saying that the place that the straw passes through the juice box is sealed? Are you assuming that the juice box is rigid? Are you saying that there was air in the top of the juice box when the box was suddenly exposed to the vacuum?

Why are you interested in this anyway?

Chet

 

[spiri]

Yes, the juice box is sealed around the straw, but the juice box is not rigid. There is no air in the juice box when exposed to vacuum.

I'm interested in determining whether ambient pressure changes would affect flow from an IV bag. The IV bag gets pressurized by gravity (in my example) and then might be brought onto an airplane, for example.

 

[Chestermiller]

So you have a balloon full of water sitting on a table, and the balloon is full and open at the neck at the top. You suddenly drop the air pressure in the room. You are interested in what happens as a result, correct?

Chet

 

[spiri]

That's correct!

 

[Chestermiller]

The short answer is "not much happens."

If the pressure is not dropped so much that the pressure approaches the equilibrium vapor pressure of the water (a few mm of mercury, so that the water boils), the volume of the liquid will increase very slightly, since water is very nearly incompressible (or expandable), and its bulk modulus is very high. The increase in volume would be less than 0.01%.

Chet

 

[spiri]

Thank you so much! That's what I was hoping happens. Would I use the ideal gas law across the inside and outside of the balloon to prove that mathematically? The changes in pressure would be less than a couple of psi.

 

[Chestermiller]

Thank you so much! That's what I was hoping happens. Would I use the ideal gas law across the inside and outside of the balloon to prove that mathematically? The changes in pressure would be less than a couple of psi.

There would be no need to use the ideal gas law. Also, inside the balloon, the liquid water is, of course, not an ideal gas. You would use the bulk modulus of water to calculate how much the volume changes if the pressure changes by a couple of psi. You can find the bulk modulus of water by Googleing it (as I did).

Chet