Fletcher wrote:
I will be introducing an anomaly I think I have found that allows my Pressure Differential/Pascal Upthrust to equalize forces at the the masses whilst allowing system equilibrium of forces as well, much as Archimedes floatation allows the trough/container vessel to balance - it involves manipulating the Hydrostatic Paradox which is why again I have emphasized it over & over.
My Solution to Finding Total System Force Equilibrium [Balance], when NOT using Archimedes uniform density distribution floatation:
General:
A. We must treat the piston masses as separate from the fluid filled lever & work the Force Profile from top to bottom.
B. Pressure & Force are quite separate but interrelated by proportion to Area.
The deeply hidden yet simple answer ?
1. the piston forces are in equilibrium with the fluid at the interface because both the pistons & the fluid exert the same pressure.
2. the pistons Weight Force is fully supported by the fluid pressure [the opposing force] i.e. their weight forces have been transmitted equally thru the fluid as undiminished fluid pressure increase & pressure is linear.
3. because the RHS piston has a smaller interface area there is an excess of upthrust from the internally contained fluid acting on the RHS of the lever - this causes CCW torque when what we want is NO System Torque i.e. Balance Conditions.
4. we want to mitigate the excess upthrust on the RHS of the lever.
5. to do this we need to reduce the downthrust on the LHS of the lever by the same amount so that the System Forces balance.
6. the 'Hydrostatic Paradox' allows us to achieve this, IINM - the paradox says that the system mass & weight will be the sum of all the masses weight forces, regardless of the shape of fluid containment or the height of the fluid column - IOW's, forces acting against internal surfaces cancel out to a net force & internal bottom pressure is only conditional upon density & height N.B. fluid pressure acting normally to any surface is a vector force of magnitude & direction, whilst pressure is scalar.
7. by inserting a solid displacer [same density as fluid] into the fluid on the LHS we are able to manipulate the Hydrostatic Paradox to an advantage N.B. fluids have scalar pressure but when in contact with a surface this quantity is expressed as a force vector at right angles to that surface - the solid displacer reduces the downthrust force on the LHS in equal & opposite magnitude to the excess upthrust on the RHS causing System Equilibrium of Forces.
Notes:
Follow the logic carefully.
Yes, it works in simulation & system balancing is achieved.
The sim was built from the above principles, anyone else can sim it too.
-fletcher