Mathematical Analysis of an Ideal ZED

[mondrasek]

MarkE, you introduced a rate into an Energy calculation.  Rate does not apply when calculating the Energy leaving the system as the piston rises in this case. 

The correct Energy = F*ds reduction for the case of the riser lifting the water on top of the piston is simply F_ave*S.

The Force starts at the maximum buoyancy Force that can be calculated from State 2.  It then declines linearly to exactly zero which is the case in State 3 since the water is flowing off of the piston as it is rising.  This is a straight forward calculation and involves no rates.

[MarkE]

No, MarkE.  And after checking, I think we need to return to your "correction" to post #667.  There you introduced a "rate" into that Energy equation.  You will need to explain that.

Do you or do you not understand how to integrate in order to obtain energy?

[MarkE]

Not to sound to silly,, but would that then suck the water up AR6 and over into AR5?

No, opening the pod chamber would allow water to flow back from AR6 into AR7.  It's just a collapsing balloon. 

[TinselKoala]

Don't forget that the atmosphere outside the system is pushing with a constant pressure. Nothing the apparatus does can affect this pressure. The outer surface area of course changes, the volume that displaces air outside changes, and there IS measurable "air buoyancy" from the displaced outer air.... but the outer air is not an "ideal gas" in the sense that the apparatus cannot store energy in the outer air, nor extract energy from it. This is because changes in the apparatus volume do not cause changes in the pressure of the outside air. And if the inner fluids of the apparatus are incompressible, then also changes in the outside air pressure do not cause changes in the apparatus volume. By having two incompressible fluids in your apparatus you have killed all chances of taking advantage of the Cartesian Diver effect, and also the submarine's manner of altering  buoyancy by pumping compressed air into and out of tanks to empty and fill them with water.

So.... how are you going to "turn buoyancy on and off"?

[mondrasek]

Do you or do you not understand how to integrate in order to obtain energy?

MarkE, we appear to have cross posted.  Please see my post previous to yours.