Has An Important Property Of Fluids Been Overlooked ?

[Red_Sunset]

............................................I include a couple of drawings in a series for you & others to work thru - the hypothesis is that buoyancy force is solely dependent on pressure differentials & not on volume displacement & uniform density doctrine.
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Hi Fletcher,
Thanks for the nice graphical representations, I feel obliged to reciprocate with the same clarity, that is good.
I think I am getting closer to your logical reasoning and I think I can see the subtle detail that escaped me, but this detail also appears to be the Achilles heel that drives the spike into the wheel of progress.
The graphical details shown in your last post #41 does not represent the piston in your original design.  Your original design has no snorkel or water head.   By not having a self regulating water head, also means you do not have buoyancy and associated behavior (that doesn't mean it can not be designed in), but as it stands now, it is pure hydraulics and that will not work as you thought of.
I see it as a mix-up between the behavior of Buoyancy & Hydraulics,  the picture below show the difference withing the context, I believe it is self explanatory

[fletcher]

Michel .. I found some time this morning - follow the drawings thru I provide as attachments to this post.

I am proposing a new type of balancing mechanism - you might think of it like a Roberval Balance but doesn't required a vertical anchored post.

Forces are fundamental to our universe - you will need to do force analysis.

-fletcher

[Red_Sunset]

Michel .. I found some time this morning - follow the drawings thru I provide as attachments to this post.
I am proposing a new type of balancing mechanism - you might think of it like a Roberval Balance but doesn't required a vertical anchored post.
Forces are fundamental to our universe - you will need to do force analysis.
-fletcher

Hi Fletcher,
Sorry this turned into a long write-up, my previous post might have been too short to get the point across.
From my viewpoint, you see the problem incomplete and a mix-up between apples and pears.  Sure buoyancy is pressure that keeps the object floating but it also automatically implicates the other Archimedes concepts of displacement...ect, even in the paradox, there is no getting away from it. (it is no different for Wayne's Zed as a Hydro device with its weightless virtual displacement). There should be no doubt that our physics laws are correct. Although it is just a question of finding ways around it that satisfies all criteria, a thinking process of trying to fool Archimedes and Nature !
Your desired objective is based on the physics rule of pressure as in buoyancy, but your implementation, by progressively removing things in your drawings took you all the way to hydraulics. You would still like to call it buoyancy in order to enjoy some of the Archimedes buoyancy benefits, aaaai that is a bit of a far stretch if you do not satisfy all necessary criteria, this is a tuff inventive bridge to cross that will need more thinking.
Weight for fluid substitution is an Archimedes buoyancy property, handled by the displacement rule that received a call from the pressure rule.

To see this more clearly, see the observation in two frames. (attached picture should makes this more clear)
Frame 1.. Pressure distribution of fluid within the holding vessel.
Frame 2.. Weight distribution of the whole picture, "vessel+liquid+object"
** You will see that pressure within a vessel doesn't equate necessary to weight outside the vessel. Because the pressure is always the same by depth (or height), regardless of the floating weight.
The pressure distribution does not have to synchronize with the weight distribution or visa versa, inside or outside the container (vessel). Several other factors come into play for weight distribution as shown in the attached picture.

Looking at the pictures provided in your post
A good show of progression, your main focus is the integral balance of weight and fluid. Looking at the plausibility of the other detail depicted, I can gather that the weight shown equals the full vertical segment of the piston in fluid weight (pict#4-5).

Forgive me for highlighting all my observations, even if several of them have no relevance to the purpose of discussion, Only done for the purpose of accuracy and to ensure I do not overlook or ignore important detail

Buoyancy_Experiments #3:    All picture shown are realistic & plausible

Buoyancy_Experiments #4:    All picture shown are realistic & plausible
Pict#4-6  -  is heavier to the left and should tilt according (piston water + weight)

Buoyancy_Experiments #5: 
All pictures should tilt to the left because "piston area water weight" + "weight of block" make left side heavier than the right side

Buoyancy_Experiments #6: 
Pict#6-1&2  -  Tilt to the left
If brown weight is the same than green weight
Pict#6-3 -   Tilt to the left
Pict#6-4 -   balanced

Buoyancy_Experiments #7: 
Pict#7-1  -  The pepette water column creates a buoyancy similarity that will provide a pressure that is limited or enhanced by the air pressure contained in the gas bag.
* The pressure with the pipette in vertical position would be  Water Column weight + gas pressure.
* The pressure with the pipette in horizontal position would be just gas pressure.
Although we can play with pressure, it does nothing in regards with the external weight balance because the weight is not floating in the liquid.
Pict#7-2  -  A capped snorkel stops to provide pressure once any demand is made due to vacuum creation at the place where the gas bag should have been
Pict#7-3  -  Here the piston is lying on top of the liquid and is held in place by the fluid that has not other place to go to.  Buoyancy does not come into play here. It is a clear hydraulic piston configuration.
A central positioned pepette would takes us back to Pict#7-1 or 2.

The main difference between hydrostatic buoyancy and hydraulics is how the upwards force is achieved.

In buoyancy,
The upwards force is achieved through the height of the water column.
It doesn't matter if this water column is created in the space between the vessel wall and the object or an open pepette within, or a distance away. The water column height is proportional to the weight of the floating object and is self regulating.
If the floating object increases in weight, so does the water column (look at a ship being loaded at the dock, it sinks deeper as more weight is loaded).
If the weight is not evenly placed within the floating object, the buoyancy will adjust automatically to this balance change. The side of the more weight must have more upward pressure, to regulate more upward pressure, the float must sink deeper into the water in the area of more weight to receive more pressure.  ( for the ship being loaded unevenly, you would see the more weighty side deeper in the water). 
What is notable,
1.. To observe is that the floating object sinks when the water column  height increases to a point larger than the freeboard (water level becomes higher than the top of the floating object)
2.. Pressure is proportional to depth and on each depth level is evenly distributed throughout the fluid, no matter the size of the float, weight or position of the weight.
3.. Weight distribution is measured by pressure and is determined by depth and is therefore evenly distributed on every horizontal plane throughout the fluid vessel. The weight distribution over the whole inside bottom will measure the same.
4.. The weight distribution of the combined "vessel+fluid+float+weight" as measured on the outside bottom of the fluid housing is proportional to the total vertical weight of each measurement square (assuming a symmetrical fluid vessel).  Since the heavier side of the floating object is compensated for by being deeper submerged, each measurement square will measure identical regardless of the location of the floating object and its weight.

In hydraulics,
The upward force is created by the fluid inability to compress and having nowhere to go to equalize the pressure. Therefore a weighted piston on top of a liquid in a closed vessel will increase the pressure in the liquid proportionate to the weight and area.  Increasing the weight will increases the pressure.
An position change due to uneven piston loading is dependent on the flexibility of the piston, piston housing and build,  a rigid device will prevent any positional change due to an uneven weight on top of the piston.
What is notable,
1.. To observe is that the piston can never sink no matter how much weight is loaded on the piston (except when the device breaks due to overloading)
2.. Pressure is evenly distributed throughout the fluid, no matter the size of the weight or position of the weight.
3.. Weight distribution measured by pressure on the inside bottom of the piston and bottom of the fluid housing is determined by the pressure and is therefore evenly distributed
4.. The weight distribution of the combined, " vessel+fluid+piston+weight" as measured on the outside bottom of the fluid housing is proportional to the total vertical weight of each measurement square (the heavier weighted side weights more)

If I missed to see a critical point you made, let me know.
I hope this helps,  Michel

[Red_Sunset]

Michel .. I found some time this morning - follow the drawings thru I provide as attachments to this post.
I am proposing a new type of balancing mechanism - you might think of it like a Roberval Balance but doesn't required a vertical anchored post.
Forces are fundamental to our universe - you will need to do force analysis.
-fletcher

Hi Fletcher,
To mention a critical point, using the right words, (to supplement previous drawings)

For an object to merge into a fluid and be identified as one mass with that fluid,  it needs to be submerged into that fluid to its floatation point, so its weight will equal the displaced water weight. At this point the water line would have increased to accommodate the displacement water.
This action would be impossible in a confined space completely filled with fluid.  Fluid expansion needs to happen to absorb the additional weight.  This is because the weight absorption/distribution by a fluid is part of the fluid displacement properties.
Regards, Michel

[Red_Sunset]

A dilemma of balance between a buoyancy and hydraulic example.
What is the overall gravity balance of the Hydraulic piston assembly that is loaded with a weight to one side ?  The hydraulic cylinder is installed with a piston floor to measure the weight distribution inside and out.
How could the hydraulic example measure more weight on the right side than the left with an even pressure distribution in the fluid.?
Do you have an explanation as compared to the buoyancy example ?