# Balloon Pressure

1. Feb 28, 2014

### Jimmy87

1. The problem statement, all variables and given/known data
We were given homework to explain how this balloon pressure experiment works. You basically take a plastic bottle and make a small hole in it near the base. You then push a balloon in through the top and pull it over the bottle opening. You then blow it up so that it inflates inside the bottle. You then immediately plug the hole you made with your finger and it remains inflated in the bottle despite the balloon being open to the atmosphere. We have to discuss the pressure:

Inside the bottle
Outside the bottle
Inside the balloon

2. Relevant equations

None

3. The attempt at a solution
I have read up online which says that the pressure inside the bottle will be lower as air is pushed out of the bottle as you inflate it. The pressure outside the bottle is higher which keeps it inflated. but when thinking about the pressure inside the balloon I don't understand why it stays inflated and no-one seems to mention pressure inside the balloon online. The pressure inside the balloon surely must be greater than outside the balloon. In order to blow up a normal balloon apparently you need 1 psi pressure to overcome the elastic forces of the balloon (i.e. a normal balloon has a higher pressure inside it). So if the air inside the balloon is greater than outside the balloon shouldn't it deflate regardless of whether the pressure inside the bottle is lower?

Thanks for any guidance offered

2. Feb 28, 2014

### voko

Because the balloon is open into the atmosphere, the pressure inside it is equal to atmospheric. Now consider the air that is in the bottle outside the balloon. Just before you plugged the hole with your finger, what was the pressure there? What is the pressure there after the balloon is opened?

3. Feb 28, 2014

### BvU

I inserted the dots; I thought about inserting the word pressure, but that is probably not what you mean, right? What do you mean there ?

I love the experiment and I like it that you did some research and came up with the 1 psi. I think that's what voko hinted at.

I'm in my study and don't have a balloon at hand. (also it's bedtime). But: as an experimental physicist I can think of an extra step in the experiment: after blowing up the balloon, plug the top bottle opening. Then the bottom hole and then unplug the top bottle opening. I bet the balloon contracts a little! Meaning the pressure difference between outside and inside of the balloon is less than 1 psi ! And before it is completely floppy it stops deflating, meaning the difference is near 1 psi again ! But the inside of the balloon is open to the outside world, so the pressure inside the balloon is equal to ..

Back to voko again!

But not without other proposals for further experimentation: can you easily re-inflate the balloon with the bottom hole still plugged? What if you did all this with the bottle in a bucket of water ?

4. Mar 1, 2014

### Jimmy87

Thanks for your replies. I'm still a bit confused. I kind of get that the air pressure inside the balloon must be equal to the outside pressure but I really can't see how that's possible if you need over pressure to blow up a balloon. Any inflated balloon has an air pressure greater than that outside. So how can they be equal?

To answer your questions, wouldn't the air pressure just before you plug it be the same as after you plug it which is a lower pressure than inside the balloon? What do you mean by after the balloon is opened?

BvU's questions - if you had the bottom hole plugged then you couldn't blow it up I think because the air can't move out the way to enable the balloon to inflate. Not sure about what would happen in a bucket of water?

5. Mar 1, 2014

### BvU

Air can't move out, but you can compress it (by at least 1 psi, and perhaps even 2!) That way the air volume outside the balloon inside the bottle becomes smaller. Bottle stays the same, hence balloon gets bigger ! Isn't it a good idea to trry it out ?

6. Mar 1, 2014

### voko

Spot on! What does that tell you about the pressure of the air that is inside the bottle but outside the balloon?

The process has the following stages.

1. The balloon is inside the bottle, not inflated.

2. The balloon is inside the bottle, inflated, the balloon's opening is held closed, the hole in the bottle is open.

3. The balloon is inside the bottle, inflated, the balloon's opening is held closed, the hole in the bottle is blocked.

4. The balloon is inside the bottle, inflated, the balloon's opening is open, the hole in the bottle is open.

It is interesting to compare pressures in the bottle (outside the balloon) at stages 2, 3, and 4, in the light of your observation about the overpressure.

7. Mar 1, 2014

### Jimmy87

Thanks for the replies. Ok so I tried it out. I blew up the balloon then quickly put my hand over the top of the bottle then (still doing this) covered the hole at the bottom. When you release your hand off the top a little bit of air comes out so would this be the over pressure? But if after this the balloon air pressure and atmospheric pressure are the same then why doesn't the elastic force of the balloon push the air out?

Also, what causes a balloon to collapse when you blow it up normally (outside a bottle) then release it? Most sources online say it is because of the higher pressure in the balloon but as demonstrated with the above experiment it is only a small over pressure. So would it be a combination of the air pressure outside pushing in on the balloon, the over pressure and the elastic forces?

8. Mar 1, 2014

### voko

It seems to me that you are confused about what "overpressure" means. Can you explain what it is?

9. Mar 1, 2014

### Jimmy87

When you blow up a balloon you need a certain amount of pressure to overcome the elastic forces of the balloon which is why an inflated party balloon has a higher pressure inside it than the atmospheric pressure outside. Is that right? For that bottle experiment, I can see that the pressures inside the balloon must be equal to atmospheric pressure otherwise it would deflate but I just don't see how it does work because surely you have the elastic forces of the balloon always acting to deflate it?

10. Mar 1, 2014

### voko

So, would it be correct to state this mathematically: $P_{\text{internal}} = P_{\text{elastic}} + P_{\text{external}}$?

11. Mar 1, 2014

### Jimmy87

Thanks Voko. Yeh I suppose it's better now you have put it in an equation like that.

12. Mar 1, 2014

### Jimmy87

Just one last thing sorry. When the balloon is inflated inside the bottle, is the pressure inside the bottle lower like I initially said. I know that air is being pushed out of the bottle as you blow it up but the volume of the inside of the bottle is also decreasing as the balloon inflates. So is the air outside the bottle at a lower pressure or not?

13. Mar 1, 2014

### voko

I suggest you go through steps 1, 2, 3, 4 above and try to say what all those P's might be like in every case.

14. Mar 1, 2014

### Jimmy87

1. The balloon is inside the bottle, not inflated. - pressure in balloon, bottle and outside bottle are the same?

2. The balloon is inside the bottle, inflated, the balloon's opening is held closed, the hole in the bottle is open. - pressure outside balloon + inside the bottle are the same? Pressure inside the balloon is greater?

3. The balloon is inside the bottle, inflated, the balloon's opening is held closed, the hole in the bottle is blocked. Think this is the same as above?

4. The balloon is inside the bottle, inflated, the balloon's opening is open, the hole in the bottle is open. pressure inside the bottle + outside are the same. Pressure inside the balloon is higher so it deflates?

Are any of those right? Pressure is the worst part of my physics and it has always confused me so apologies for the continually slow up take. Thanks for any help

15. Mar 1, 2014

### voko

Correct. Observe that all that parts communicate freely with the atmosphere, so the pressure has to be the same everywhere.

Even if we assume it is the same, what is this pressure? try to reference it with the atmospheric pressure. Then think whether that little formula above is satisfied.

Correct. By plugging the hole in the bottle we don not change the pressure anywhere.

Again: what is this (and other) pressure? Try to reference them with the atmospheric pressure. Then think whether that little formula above is satisfied.

16. Mar 1, 2014

### Jimmy87

2)Pressure inside bottle + outside are the same and are at atmospheric pressure. Pressure inside balloon is greater than atmospheric pressure? The pressure inside the balloon has to overcome this atmospheric pressure + the balloons elastic pressure so must be greater than atmospheric pressure?

4)Pressure inside the bottle + outside are the same (which is atmospheric pressure) and balloon has greater than atmospheric pressure. Now you release both holes, the air in the balloon will leave because the pressure is higher?

17. Mar 1, 2014

### voko

Good!

Do we release both holes? That would bring us to case 1).

18. Mar 1, 2014

### Jimmy87

Thanks again for your help. So if both holes are released we go to case 1 which means the balloon must be fully deflated. So to go from inflated just before you open both holes to fully deflated air must come out of the balloon. I'm not sure whether air leaves when both holes are open because the air inside the bottle forces it to or because the elasticity of the balloon forces it to or both? The instant you open both holes the inside of the bottle is still at atmospheric pressure and so is the air above the opening so I'm thinking then it must just be the elasticity of the balloon? Could you clarify?

19. Mar 1, 2014

### voko

Case three is when the balloon is allowed to communicate with the atmosphere, but the air trapped inside the bottle is not. What can be said about the pressures in those parts? Think of the formula in #10 while you are at that.