Effects of press on a submerged chamber w/complex sidewall

[Chestermiller]

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".

My understanding was that there is air inside the bellows connected by a tube to the outside air. Is this an incorrect interpretation?

Chet

 

[russ_watters]

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.

Your response doesn't fit the help you've gotten: you've received no chastizement, only help -- but only as much help as is possible given that you aren't trying very hard to help us help you.

 

[russ_watters]

My understanding was that there is air inside the bellows connected by a tube to the outside air. Is this an incorrect interpretation?

No, it looks like I misread: I saw "inlet pipe" and thought that meant it must be a water pipe. But it does say atmospheric pressure.

So then my answer is that the bellows opens when the balloon has inflated enough that the buoyant force is greater than the downward pressure on the plate. And the sidewalls have no impact if they are designed to be very flexible.

 

[mfb]

@Chestermiller: pressure on the plate is $p=\rho g h$ with the water height h and density $\rho$, force is simply this multiplied by the area: $F_p=A\rho g h$. Buoyancy is given by $F_b=V \rho g$. Setting both equal gives $V=A\cdot h$. Naturally the height of the balloon is limited by h and it won't have a perfect rectangular shape, which means the balloon needs an area larger than A. You can consider the extreme case where it exactly fills up the volume above the plate, then we don't have to consider water at all (neglecting the mass of the plate itself and the bellows).

The bellows might bend inwards (or reduce their volume from the parts pointing outwards), and do so more if they are extended more. This would lead to an additional force upwards for the movable plate.

 

[montoyas7940]

@Chestermiller: pressure on the plate is $p=\rho g h$ with the water height h and density $\rho$, force is simply this multiplied by the area: $F_p=A\rho g h$. Buoyancy is given by $F_b=V \rho g$. Setting both equal gives $V=A\cdot h$. Naturally the height of the balloon is limited by h and it won't have a perfect rectangular shape, which means the balloon needs an area larger than A. You can consider the extreme case where it exactly fills up the volume above the plate, then we don't have to consider water at all (neglecting the mass of the plate itself and the bellows).

The bellows might bend inwards (or reduce their volume from the parts pointing outwards), and do so more if they are extended more. This would lead to an additional force upwards for the movable plate.

OP says no.

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.

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?

 

[mfb]

Well, at least it deforms according to the accordion structure getting unfolded.

 

[montoyas7940]

according to the accordion

I see what you did there...

 

[Chestermiller]

@Chestermiller: pressure on the plate is $p=\rho g h$ with the water height h and density $\rho$, force is simply this multiplied by the area: $F_p=A\rho g h$. Buoyancy is given by $F_b=V \rho g$. Setting both equal gives $V=A\cdot h$. Naturally the height of the balloon is limited by h and it won't have a perfect rectangular shape, which means the balloon needs an area larger than A. You can consider the extreme case where it exactly fills up the volume above the plate, then we don't have to consider water at all (neglecting the mass of the plate itself and the bellows).

Thanks mfb. As it turns out, I realized this a little later after reading your post.

Still, if the balloon inflates at all, it's going to reduce the downward force on the upper plate a little, and it might move up a little bit.

The bellows might bend inwards (or reduce their volume from the parts pointing outwards), and do so more if they are extended more. This would lead to an additional force upwards for the movable plate.

Yes. I think that analyzing the structural mechanics of the bellows response would be the only complicated part of modeling this problem. There is going to be bending at the crimp locations (and a small amount in-between), and the geometry of the exposed surface to the surrounding water pressure is going to change a little. This can probably be analyzed using Strength of Materials considerations, but, as a last resort, there's always finite element (for the bellows only). But I'm sure that the basics of the structural mechanical response of bellows has been reported in the literature.

Chet