# pressure difference at concave side of bubble

#### ling233

I was told that the pressure difference at concave side of bubble is higher , why is it so ?

#### Attachments

• 352.1 KB Views: 7

#### ChipB

PHF Helper
For a thin shell sphere the stress in the shell can be assumed to be constant across its thickness. That seems to be what the figure is saying, although I don't understand the first factor of 2 in the stress (sigma) portion of the free body diagram - I would think that term should be thickness of the bubble, so that the units work out to force.

In thick shell spheres the stresses are indeed highest at the inside surface of the shell. This is why when inspecting a pipeline for structural integrity you have to send a camera into the pipe to check the interior walls, as that is where cracks will first form.

#### ling233

For a thin shell sphere the stress in the shell can be assumed to be constant across its thickness. That seems to be what the figure is saying, although I don't understand the first factor of 2 in the stress (sigma) portion of the free body diagram - I would think that term should be thickness of the bubble, so that the units work out to force.

In thick shell spheres the stresses are indeed highest at the inside surface of the shell. This is why when inspecting a pipeline for structural integrity you have to send a camera into the pipe to check the interior walls, as that is where cracks will first form.
i have one more question here . I was also told that the pressure at the concave side of the bubbles is higher ... why is it so ? is it because of the circumference of the pressure at the concave side is higher?

#### ChipB

PHF Helper
I have one more question here . I was also told that the pressure at the concave side of the bubbles is higher ... why is it so ?
You have used the word "pressure" but I assume you mean stress. In other words you are asking why stress in the shell of a spherical pressure vessel is higher along the inside of the shell than on the outside - is that correct? As I noted earlier, for a thin shell like a bubble the stress is essentially constant across the width of the shell wall. Where did you hear that the stress in a bubble is higher on the inside than the outside?

is it because of the circumference of the pressure at the concave side is higher?
Sorry, but I don't understand what you are trying to say here. Pressure doesn't have a circumference.

The mathematics of calculating stress in a spherical thick shell is quite complicated, and so in practice one would likely use a finite element technique to model the stress distribution. But think about how with increasing radius in the shell wall the forces that are pressing outward are distributed over a larger area of the shell, so consequently the stress (force per unit area) in the shall gest smaller. This really only applies to thick shells - for a thin shell like a bubble the stress across the width of the shell is essentially constant.

Last edited:

#### ling233

You have used the word "pressure" but I assume you mean stress. In other words you are asking why stress in the shell of a spherical pressure vessel is higher along the inside of the shell than on the outside - is that correct? As I noted earlier, for a thin shell like a bubble the stress is essentially constant across the width of the shell wall. Where did you hear that the stress in a bubble is higher on the inside than the outside?

Sorry, but I don't understand what you are trying to say here. Pressure doesn't have a circumference.

The mathematics of calculating stress in a spherical thick shell is quite complicated, and so in practice one would likely use a finite element technique to model the stress distribution. But think about how with increasing radius in the shell wall the forces that are pressing outward are distributed over a larger area of the shell, so consequently the stress (force per unit area) in the shall gest smaller. This really only applies to thick shells - for a thin shell like a bubble the stress across the width of the shell is essentially constant.
here is it . pls refer to the second photo ( the pressure 'jump' at the last few lines. Not 'stress'

#### Attachments

• 152.8 KB Views: 2
• 231.1 KB Views: 2
• 231.4 KB Views: 1

#### MBW

The surface of a liquid exerts a surface tension.
this is due to the attraction between the atoms or molecules of the liquid being higher to each other than to the atoms or molecules of the surrounding medium.
This surface tension is trying to collapse the bubble, but can't because of the pressure of the air trapped inside it.
However this means that the surface tension trying to collapse the bubble will increase the pressure of the air inside the bubble relative to the air outside the bubble.
The bubble is just like a balloon, the surface is stretched and is trying to unstretch itself, and the air inside is under pressure and is pushing back to balance the situation.

#### ChipB

PHF Helper
here is it . pls refer to the second photo ( the pressure 'jump' at the last few lines. Not 'stress'
Now I understand your question - you totally threw me with the original figure you posted, which has to do with stress in the walls of a thin shell. Why did yo post that figure?? Now you are asking about the air pressure inside a bubble compared with air pressure outside the bubble. It should be pretty obvious - to balance forces the air pressure inside has to counteract the air pressure outside plus the tensile forces of the bubble itself, which means the air pressure inside is greater than the air pressure outside. Like blowing up a rubber balloon - prior to blowing air into it the air pressure inside equals the air pressure outside, and the balloon is limp. To blow it up you have to force air into it, and the pressure inside becomes higher than the air pressure outside - this is made pretty obvious by the fact that you have to keep the neck of the balloon inched closed or else the air will rush out of the balloon. Stated another way: the air pressure against the inside concave surface of the bubble is greater than the air pressure against the outside convex surface of the bubble - otherwise there would be nothing to keep the bubble from collapsing under its own weight.