Effects of press on a submerged chamber w/complex sidewall

[morfzcspls]

I would like to show the details of the situation before asking the specific question so:

Conditions:The attached sketch shows a situation that is slightly after the start, since the balloon is shown with air already inside. The question that I will ask is about a situation where the balloon is completely empty to start with. Note: the pressure required to fill the balloon is not a factor.The chamber is circular with an accordion fold sidewall that will not deform or twist due to the water pressure against it, but still acts like an accordion and the chamber is fixed to the bottom of the tank.The top plate of the chamber has zero buoyancy and is attached to the bottom plate by the sidewall so that the chamber is airtight within the tank.
QUESTION:The question is what volume of air would be needed to supply enough buoyancy in the balloon to create suction in the inlet pipe protruding from the bottom of the chamber to atmospheric pressure?

 

[berkeman]

Nice drawing! :-)

What is the context of the question? What does this mechanical setup do?

 

[russ_watters]

I don't get it either:
1. Is the whole apparatus underwater?
2. Where does the water come from to fill the "chamber"? By that, I mean, what is the pressure?

 

[montoyas7940]

It appears as though the balloon is inside a 3x15 ft. sealed box with an "accordian" bottom end. Right?

If that is the case, adding volume to the balloon will push the bottom down due to the increased water pressure in the box.
So, no suction. You will have discharge instead.

 

[Bandersnatch]

It appears as though the balloon is inside a 3x15 ft. sealed box with an "accordian" bottom end. Right?

If that is the case, adding volume to the balloon will push the bottom down due to the increased water pressure in the box.
So, no suction. You will have discharge instead.

Note that the accordion top is the part that is 3 ft wide(radius?). The size of the tank is unspecified, so (I think) it can be made arbitrarily large to accommodate a balloon of a much larger diameter than the accordion.

 

[montoyas7940]

Note that the accordion top is the part that is 3 ft wide(radius?). The size of the tank is unspecified, so (I think) it can be made arbitrarily large to accommodate a balloon of a much larger diameter than the accordion.

Oh! I see that now. So it is a bouyant force vs force due to pressure issue?

No... Intuitively I think chamber vs. accordian size doesn't matter. If the volume of the balloon increases and the chamber is sealed the bottom must move down.

But we don't know if it IS sealed. Do we? Or am I missing it?

 

[Bystander]

don't know if it IS sealed. Do we?

There is a different line weight/shade at the top, consistent with an open top, but it isn't unambiguous.

 

[Chestermiller]

This sounds suspiciously like a homework problem. Is it? If so, it should have been posted in the homework forum, using the required template. Also, if it is a homework problem, it should have an exact problem statement that you can provide word for word. You are wasting people's time keeping them guessing about the problem statement. I expect you to provide an exact problem statement.

Chet

 

[russ_watters]

This sounds suspiciously like a homework problem.

I was going to guess perpetual motion. Want to bet one "prop"?

 

[morfzcspls]

Nice drawing! :)

What is the context of the question? What does this mechanical setup do?

Hi berkeman,The drawing is derived from a concept that I am working on and the mechanical setup by itself has no purpose. It is just a creation that allows me to clearly ask the question. What I am trying to understand is how the folds in the sidewall change the amount of force required to expand the chamber. I think a discussion of the details surrounding this question would be interesting in general and will certainly help me out.
Thanks’

 

[morfzcspls]

I don't get it either:
1. Is the whole apparatus underwater?
2. Where does the water come from to fill the "chamber"? By that, I mean, what is the pressure?

The chamber and the balloon are 15 ft below the surface of the tank, and the question is asked when the tank is already full. The pressure at 15 ft is approximately 6.48 PSI

 

[Bystander]

The only force you'll be getting is from the "spring constant of the bellows." Google that first.

 

[morfzcspls]

It appears as though the balloon is inside a 3x15 ft. sealed box with an "accordian" bottom end. Right?

If that is the case, adding volume to the balloon will push the bottom down due to the increased water pressure in the box.
So, no suction. You will have discharge instead.

Sorry for the confusion montoyas7940,

The tank diameter is not defined and the tank is open at the top. The chamber consists of a 3 ft dia top and bottom plate (crosshatched in the sketch). Are you saying that there is no amount of air (assuming the tank can't overflow) that will lift the top plate. Also assuming that the balloon will never touch the sides of the tank, again sorry for the poorly described situation.

 

[morfzcspls]

Note that the accordion top is the part that is 3 ft wide(radius?). The size of the tank is unspecified, so (I think) it can be made arbitrarily large to accommodate a balloon of a much larger diameter than the accordion.

Thanks Bandersnatch,

Due to the poorly described situation that I presented I need all the help I can get.

 

[morfzcspls]

This sounds suspiciously like a homework problem. Is it? If so, it should have been posted in the homework forum, using the required template. Also, if it is a homework problem, it should have an exact problem statement that you can provide word for word. You are wasting people's time keeping them guessing about the problem statement. I expect you to provide an exact problem statement.

Chet

Sorry Chestermiller,

This has nothing to do with homework I assure you, and I apologize for my Inability to succinctly state the question but it was my intention to do so. I attempting to create a discussion about how the accordion fold sides effect the force required to lift the top plate etc. By the way I haven't seen the inside of a classroom for of 30 years.

 

[montoyas7940]

The chamber and the balloon are 15 ft below the surface of the tank, and the question is asked when the tank is already full. The pressure at 15 ft is approximately 6.48 PSI

Is the tank also submerged? Partially, completely? How does the water level inside compare to the level outside? Equal due to the accordian - I would think.

 

[morfzcspls]

Oh! I see that now. So it is a bouyant force vs force due to pressure issue?

No... Intuitively I think chamber vs. accordian size doesn't matter. If the volume of the balloon increases and the chamber is sealed the bottom must move down.

But we don't know if it IS sealed. Do we? Or am I missing it?

The bottom of the chamber is attached to the bottom of the tank and the chamber is sealed against the contents of the tank but open to atmosphere through the bottom of the tank. So are you saying that the top plate will move down? Also since the accordion fold side offer a surface to the ambient pressure it seems it would have to be considered.

 

[morfzcspls]

Is the tank also submerged? Partially, completely? How does the water level inside compare to the level outside? Equal due to the accordian - I would think.

Sorry, I should have added that the tank is not submerged in my last response.

 

[morfzcspls]

The only force you'll be getting is from the "spring constant of the bellows." Google that first.

Are you saying, assuming that the chamber and the balloon start out fully collapsed, that no amount of air pushed into the balloon will move the top plate?This may seem simple to you but I am having a hard time understanding it.

 

[Bystander]

move the top plate?

You'll be able to lift the top plate with a large enough balloon. I meant only that the sidewall will have no effect beyond the spring constant of the bellows.

 

[morfzcspls]

You'll be able to lift the top plate with a large enough balloon. I meant only that the sidewall will have no effect beyond the spring constant of the bellows.

Since the accordion fold side presents surfaces to the ambient pressure it seems that it needs to be considered. If so the number of folds becomes important and how they are allowed to unfold could also be important if there were many folds.

 

[Bystander]

If so the number of folds becomes important and how they are allowed to unfold could also be important if there were many folds.

Only the total "normal" cross-sectional area (normal being in the direction you're stretching/expanding the bellows). Numbers and areas of folds have NO effect.

 

[morfzcspls]

Only the total "normal" cross-sectional area (normal being in the direction you're stretching/expanding the bellows). Numbers and areas of folds have NO effect.

Thanks for the help Bystander,

I have gained some good information to work with from all you guys.

 

[montoyas7940]

So are you saying that the top plate will move down?

If the tank (not chamber) is a sealed volume, yes. But you said it is not. Is there room at the top for the water level to rise or will it spill over as the balloon inflates?

EDIT: sorry, I see where you said the tank is full. So the water will spill out as the balloon inflates...

 

[morfzcspls]

If the tank (not chamber) is a sealed volume, yes. But you said it is not. Is there room at the top for the water level to rise or will it spill over as the balloon inflates?

EDIT: sorry, I see where you said the tank is full. So the water will spill out as the balloon inflates...

Again sorry for not being clear, since I have been kicking this around for awhile now it is all so obvious in my head.

The tank has sufficient room at the top for expansion without overflow and it has a large enough diameter so that the balloon will never touch the sides.

 

[montoyas7940]

Okay, I see. Then there may be a bouyant force sufficient to overcome the static force on the accordian chamber.

Imagine what would happen if the tank were full and had a top with a long 1" vertical pipe plumbed into and rising above it. When you increased the balloon volume the water level would rise rapidly up the pipe increasing static pressure on the accordian chamber.

 

[morfzcspls]

Okay, I see. Then there may be a bouyant force sufficient to overcome the static force on the accordian chamber.

Imagine what would happen if the tank were full and had a top with a long 1" vertical pipe plumbed into and rising above it. When you increased the balloon volume the water level would rise rapidly up the pipe increasing static pressure on the accordian chamber.

Anyway, I have some things to think about from you guys so I’m going to start hacking away at my concept.Thanks

 

[berkeman]

Hi berkeman,The drawing is derived from a concept that I am working on and the mechanical setup by itself has no purpose. It is just a creation that allows me to clearly ask the question.What I am trying to understand is how the folds in the sidewall change the amount of force required to expand the chamber. I think a discussion of the details surrounding this question would be interesting in general and will certainly help me out.
Thanks’

It looks a bit like you are wanting to discuss a perpetual motion machine (PMM) mechanism. That sort of discussion is not allowed on the PF. Can you please clarify what you are asking about this for?

 

[Chestermiller]

I have some thoughts on this that I'd like to add. In my judgement, the key element in this problem is the plate attached to the top of the bellows. There are several forces acting on this element:

1. The hydrostatic force on the top of the plate (if the tank doesn't overflow, this increases when the depth of liquid in the tank increases as the balloon inflates, but decreases if the plate rises). It can easily be quantified.

2. The force of air on the bottom of the plate (this will always be atmospheric).

3. The weight of the plate (since the plate is supposed to be neutrally buoyant, this means that its density is the same as that of water).

4. Balloon force on top of plate (this will be determined by the volume of air in the balloon, according to Archimedes Law).

5. Upward spring force of the bellows. This might be a little difficult to determine, since it is going to depend on both the distance between the plates and the hydrostatic pressure of the water outside the chamber (which changes). A structural analysis can be carried of the bellows (probably non-linear) spring response to these effects. Of course, alternately, it can be measured experimentally.

In any event, modelling the behavior of this system should not be overly complicated.

Chet

 

[morfzcspls]

It looks a bit like you are wanting to discuss a perpetual motion machine (PMM) mechanism. That sort of discussion is not allowed on the PF. Can you please clarify what you are asking about this for?

Is this what you guys do? We all know that the energy required to fill the balloon is equal to or greater (due to efficiency) than the buoyancy that is produced. I know my presentation was badly done but the question seems straight forward enough, but the only thing that I have received so far is questions and chastisement. Not one attempt to answer the basic question of what affect the accordion fold sidewall has on the force required to lift the top plate of the chamber.

Please forgive me for attempting to ask this obviously offensive and seemingly insoluble question.

 

[Chestermiller]

Is this what you guys do? We all know that the energy required to fill the balloon is equal to or greater (due to efficiency) than the buoyancy that is produced. I know my presentation was badly done but the question seems straight forward enough, but the only thing that I have received so far is questions and chastisement. Not one attempt to answer the basic question of what affect the accordion fold sidewall has on the force required to lift the top plate of the chamber.

Please forgive me for attempting to ask this obviously offensive and seemingly insoluble question.

Are you dissatisfied with the analysis I presented in post #29, and do feel that it is flawed? I thought I had fleshed out the problem pretty completely.

Chet

 

[mfb]

The bellows will have some small effect, depending on how exactly they unfold under pressure differences. This will look similar to a different area of the top plate.

Note that your sketch is very unrealistic. The volume of the balloon has to be equal to the surface of the plate multiplied by the height of the water (plus some smaller correction from the bellows). The balloon has to be wider than the plate (probably by some large amount), otherwise the concept will never work.

 

[Chestermiller]

The bellows will have some small effect, depending on how exactly they unfold under pressure differences. This will look similar to a different area of the top plate.

Note that your sketch is very unrealistic. The volume of the balloon has to be equal to the surface of the plate multiplied by the height of the water (plus some smaller correction from the bellows). The balloon has to be wider than the plate (probably by some large amount), otherwise the concept will never work.

Can you please explain in further detail. I don't really understand the rationale of these arguments.

Chet

 

[russ_watters]

What I am trying to understand is how the folds in the sidewall change the amount of force required to expand the chamber.

The folds in the side wall have no impact.

The pressure at 15 ft is approximately 6.48 PSI

I meant the pressure of the water entering via the tube.

For example, if the tube is connected to the side of the tank, then any amount of air in the balloon will open the "bellows".

 

[russ_watters]

2. The force of air on the bottom of the plate (this will always be atmospheric).

How do you know that?

For the others, I was assuming neutral buoyancy and a completely flexible/non-elastic sidewall, so no impacts from anything but the buoyancy of the balloon and the pressure inside the "bellows".