Undergrad What is the pressure of trapped air inside this tube?

[lost captain]

As you can see from the picture, i have an uneven U-shaped tube, sealed at the short end. I fill the tube with water and i seal it. So the short side is filled with water and the long side ends up containg water and trapped air.
Now the tube is sealed on both sides and i turn it in such a way that the traped air moves at the short side.

Are my claims about pressure in senarios A & B correct?
What is the pressure for all points in senario C?
(My question is basically coming from watching this video of the Action lab:




just saying if anyone else has seen it.)

Sorry about the quality of the picture i don't know why it degrades when i upload it

 

[jbriggs444]

Are my claims about pressure in senarios A & B correct?

Yes.

What is the pressure for all points in senario C?

Have you considered applying Boyle's law?

 

[lost captain]

Yes.

Have you considered applying Boyle's law?

Sure, the water is incomprehensible and so the trapped air exists in a fixed volume. Whether it is trapped in the long side or the short one. The volume stays the same, the temperature also doesn't change, so the pressure will stay the same, Patm?
But if that's true how is the pressure at points 1 and 3 the same?

Also thank you very much for taking the time to reply

 

[256bits]

Water can be considered incompressible for the scenario.
Thus the water volume in A or C will be the same.
What does that tell you about the volume of air, and in turn its pressure?

 

[lost captain]

Water can be considered incompressible for the scenario.
Thus the water volume in A or C will be the same.
What does that tell you about the volume of air, and in turn its pressure?

That the pressure will remain Patm?
But If you watch the video we see that the air pressure remains the same but the water pressure increases

 

[256bits]

Video

But If you watch the video we see that the air pressure remains the same but the water pressure increases

The 'system' pressure is greatest in scenario A. with the bubble at the top.

 

[lost captain]

Video


The 'system' pressure is greatest in scenario A. with the bubble at the top.

If the pressure of the air bubble stays the same then the pressure at the interface of the air and water will stay the same.
If that's true then the pressure of the water doesn't change throughout the whole volume of water, it doesn't change at the point where the water touches the trapped air

 

[jbriggs444]

If the pressure of the air bubble stays the same then the pressure at the interface of the air and water will stay the same.

Right

If that's true then the pressure of the water doesn't change throughout the whole volume of water, it doesn't change at the point where the water touches the trapped air

The second part here is correct. That means that the fluid pressure at the air-water interface is sure to be one atmosphere.

The pressures elsewhere in the fluid are not sure to be the same as this. You may have to work those pressures out using the $\rho g h$ formula. Pay attention to signs.

 

[lost captain]

Right

The second part here is correct. That means that the fluid pressure at the air-water interface is sure to be one atmosphere.

The pressures elsewhere in the fluid are not sure to be the same as this. You may have to work those pressures out using the $\rho g h$ formula. Pay attention to signs.

So in the video the claim that the pressure of the whole system increases, is wrong?

 

[jbriggs444]

So in the video the claim that the pressure of the whole system increases, is wrong?

*sigh*. Now I will need to watch the video to see what it is actually claiming...

Having watched the beginning of the video, I see that your original post described a transition from bubble at the top to bubble at the bottom. The video describes a transition from bubble at bottom to bubble at top.

I agree that a transition from bubble at bottom to bubble at top increases pressure (at any particular chosen point). Conversely, a transition from bubble at top to bubble at bottom decreases pressure.

Can you support a claim that the pressure at any fixed point within the container remains unchanged?

[I do not know what is meant by the phrases "overall pressure" or "pressure of the whole system"]

For extra credit... What happens if $h'_1$ exceeds about 10 meters?

 

[256bits]

So in the video the claim that the pressure of the whole system increases, is wrong?

To which orientation of the u-shaped tube are you referring? as having the higher system pressure.

You have the pressure at point labelled 3 in Fig 3
What is the pressure at point labelled 2?
And at point 1?

 

[DaveC426913]

To which orientation of the u-shaped tube are you referring? as having the higher system pressure.

You have the pressure at point labelled 3 in Fig 3
What is the pressure at point labelled 2?
And at point 1?

J-shaped? J naturally has a head and a tail.

Carry on.

 

[lost captain]

Conversely, a transition from bubble at top to bubble at bottom decreases pressure.

In my senario where we go from bubble at the top to bubble at the bottom if the air pressure doesn't change,meaning it stays Patm , then in fig. C the pressure at point 3 must be Patm since it's the point at the interface.
Now point 3 is also at the same height with point 1 so these two points should also have the same hydrostatic pressure since pressure depends only on height. BUT if Pressure at 1 equals Pressure at 3 then the claim of the video that the pressure of the system increases, meaning the pressure of all the points both at the top and the bottom of the tube increases is wrong.
So the claim that the pressure in any particular point will decrease if we go from bubble at the top to bubble at the bottom is wrong?

Also how can pressure at 1 be just atmospheric? Shouldn't it be P(1) = ρgh + Patm?

Thank you for watching the video

 

[lost captain]

J-shaped? J naturally has a head and a tail.

Carry on.

Yes right J shaped

 

[jbriggs444]

In my senario where we go from bubble at the top to bubble at the bottom if the air pressure doesn't change,meaning it stays Patm , then in fig. C the pressure at point 3 must be Patm since it's the point at the interface.

Agreed.

Now point 3 is also at the same height with point 1 so these two points should also have the same hydrostatic pressure since pressure depends only on height.

Agreed.

BUT if Pressure at 1 equals Pressure at 3 then the claim of the video that the pressure of the system increases, meaning the pressure of all the points both at the top and the bottom of the tube increases is wrong.

What increases compared to what?

What specific point are you claiming does not change in pressure compared to the same point with the bubble moved?

I note that points 1 and 3 moved when you changed from drawings A and B to drawing C.

Also how can pressure at 1 be just atmospheric? Shouldn't it be P(1) = ρgh + Patm?

$\rho g h$ gives the pressure difference between the top and bottom of a column of height h. If we know the pressure at the bottom of that column is atmospheric, that means that the pressure at the top of the column must be $\rho g h$ less than atmospheric.

Recall my remark about 10 meters a few posts back. What happens if $h > 10 \text{ m}$? What is the pressure at the top of the column then? You know about U tube barometers, right?

 

[lost captain]

To which orientation of the u-shaped tube are you referring? as having the higher system pressure.

You have the pressure at point labelled 3 in Fig 3
What is the pressure at point labelled 2?
And at point 1?

Well according to the video when the bubble is at the short end, then any particular point is at a lower pressure rather than when the bubble is at the long side. So the higher system pressure is with the bubble at the top of the long side.

I don't understand your question about the points 2 and 1. I'm essentially asking what is the pressure at these points

 

[lost captain]

I note that points 1 and 3 moved when you changed from drawings A and B to drawing C

Omg you are right, this is a mistake in my drawing, i must re-upload it. The right position of the points are the ones in fig.C

 

[jbriggs444]

Well according to the video when the bubble is at the short end, then any particular point is at a lower pressure rather than when the bubble is at the long side. So the higher system pressure is with the bubble at the top of the long side.

Yes, I agree with that.

I don't understand your question about the points 2 and 1. I'm essentially asking what is the pressure at these points

Prior to correcting it, I had written about points 1 and 2. I meant to refer to points 1 and 3.

In both drawings A and B, points 1 and 3 are level with the top of the hook in the J.
In drawing C, points 1 and 3 are further down at the level where the water is free to flow.

[And I see that you now realize this and are correcting it]

 

[lost captain]

What increases compared to what

Pressure increases. In my case pressure should decrease since i go the opossite way of the video. So in my senario:
when the bubble was at the top the pressure at point 1 should be higher than the pressure at point 1 when the bubble is at the bottom

Yes, I agree with that.

Prior to correcting it, I had written about points 1 and 2. I meant to refer to points 1 and 3.

In both drawings A and B, points 1 and 3 are level with the top of the hook in the J.
In drawing C, points 1 and 3 are further down at the level where the water is free to flow.

[And I see that you now realize this and are correcting it]

 

[lost captain]

Okay..i think i figured it out. Is the below correct?