OK so I'll take that at face value.

Right. So let me explain this.

I have a chamber with a piston in it which has a rod protruding out of the bottom. It is sized so that it is 0.5m tall and it contains 100l of water. I use the 1,000kg to force the water out, at 7m of depth pushing the rod against a fixed surface to create pressure, and create 90kg of buoyant force by driving the water out of the chamber. OK I have to have an air tube connected to the bottom of the chamber to avoid a vacuum and it has a 10kg effect on the whole thing. But, in the interest of brevity.

I have moved 0.5m and I create 90kg of buoyant force.

My second chamber is the same as the first, but the shaft holding the piston goes right through it and comes out the top. Sealed naturally.

What happens when I, mechanically, disconnect that 90kg of force from the weight above the water and connect it to the top of the piston on the second chamber?

Then continue the same action. New fixed surface, new piston being driven down by 1,000 kg of force, new 0.5 meters of movement. Except, that the 90kg of buoyant force pulling upwards on the top of the piston shaft.

If we continue this, assuming that the weight started this action 7 meters above the water, after 13 iterations I will have 1080kg of buoyant force. At a fall from 7m to 13.5m depth, the pressure has risen from 1.7bar to 2.3 bar. But my pressure in this chamber created by the piston is always 5kg/sq cm. Or, in other words, sufficient to expel the water at each depth.

So now I have 1080kg of buoyant force, connected to a weight which is 1000kg. the top of the buoyant force is 7m below the surface. The bottom of it is 6.5m below that. Which means the entire 6.5m long buoyancy chamber can rise 7 meters, because we started this exercise 7 meters down.

Now I'm totally confused here and, remember, I haven't even begun to calculate what each cumulative 90kg force does to the equation when acting on the top of the piston.

So, first, are my calculations correct. Do I have enough energy to expel the 100l of water from the small buoyancy chambers for each 0.5m of fall of the weight?

Second. Will the 90kg of buoyant force work with the falling weight (1000kg in the air above the water), work against it or do nothing because it is not moving

Third, why do I calculate

Energy used by falling of the 1,000kg weight as 68,670n (1000 * g * 6.5)

Potential energy of the flotation chamber as 74,163n ((pV-mg)gd or 1080 * g * 7) Even at 6.5 it would be more.

Fourth. Because I started 7m down and I have only fallen an additional 6.5m, I can rise a further 0.5m before the first chamber reaches equilibrium or the surface of the water

Fifth. If I lock the entire frame at that point where the first chamber reaches equilibrium, I can then use the buoyant force of the 6.5m long chamber to collapse and flood itself [edit] and sink back to 7m depth.

[Edit] ignore this bit.

~~Sixth. I can now fall 7m with a force of 1000kg and a series of chambers which are 0kg buoyant force in order to start again.~~

That is for later when I don’t use 5kg/sq cm

Let’s keep it as I gaind 0.5m.

OK so having put all that in, how does this match with

This requires doing work against the pressure of the surrounding water.

That amount of work should be exactly equal to the amount work extracted by the overall device. Add some friction, and you are at net negative.

Because I can tell you, for me that does not add up.

Did I get the calculation wrong. Is it not possible for the 100kg weight to expel that 100l of water at 7m depth? I calculate the pressure created as 5kg/sqcm

1000 (weight)/200 (sq cm piston)

I calculate the ambient pressure at 7m to be 1.7bar or 1.733 kg / sq cm. Which means my 5kg will always force the water out.

I calculate the final ambient pressure at 13.5m to be 2.4 kg/sq cm

I'd like someone to tell me why it does not add up. Because it's not in line with the statement above.

Also remember that in a balanced system each 90kg of buoyant force would act against the 1000kg which is pressing down. In this system it does not although, at some point, fluid dynamics would act to provide pressure against the downward force until the fluid was vented. However the net effect would still be that all force goes to creating more buoyancy, both buoyant force and the 1,000kg force above the water. Not in counteracting the original force.

So from beginning to end, the 1,000 kg force always exerts itself fully against the chamber being vented.

Please now take it apart without generic statements of a balanced system. This is not a balanced system. I'm looking for some help here to describe this.