Help to Determine Side Wall Pressure Please.

No matter how convoluted the "plate piston," when the proper trig functions are applied, various items "cancel out" so that the overall resultant forces are the same as if the plate were still flat.

If the fluid is liquid, its pressure varies with depth; if gas, essentially constant throughout the confines of the compartment.

(Were you hoping that this configuration would slide perpetually to the right?)

Pressure acts normally to ALL surfaces. If you integrate the effect on the partition plate you have a vertical force and several horizontal forces coming from the pressure effect on the "B" and "2 x B" areas. But those areas are opposite to each other so that in principle if the plate is VERY stiff their effect on the wall would be nil. Since the plate is not infinitely stiff it will be deformed in horizontal direction and will exercise on the vertical wall a force function of the ratio of the 2 stiffness: wall/plate. This force will not be ONLY directed to the right but will act as well on the left wall.

If these assumptions are completely in error:

yes its all error assumptions.

pressure is uniformly and perpendicularly affect on all surfaces independent on containers shape.

it means that upward pressure, lower ward pressure, and side walls pressure will not change. it will be P+ for upper portion and P- for lower one.

acting force upon separator plate = (P+) -( P-) X cross section area between the two walls independent on separator shape

Rotate the cylinder 90°. How much surface area do you see?

Just as all the others have explained no change due to the shape. A simple analogy would be pistons of various configurations in engines. Smaller car engines more common, you will find piston tops shaped much like your drawing.

Some medium speed diesel engines are shaped perfectly due to the fact that they actualy rotate while in motion (EMD's). But yes this is getting off topic isnt it?

I would like to add some remarks. The partition is welded to the vertical wall. Under pressure this wall will deform increasing its diameter and thus pulling in radial direction the plate. The fact that due to its geometry the plate is deformed in SAME direction will reduce the strain at the interface plate wall, it could lead to a better overall behaviour since stress level decreases. The remark about rotating is justified for external forces in your case the problem is hyper-static and deformations under load play an important role. same comment for the piston example: the piston is free from a bond to the wall since it has to slide, the only force transmission (beside the angular effect of the connecting rod) is when due to a high temperature it would expand and press the cylinder.

Thank you all for the guidance - back to the drawing board for me.

If anything comes of it I will let you know. Thank you again.

jt.

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on the shoulders of giants. (mis-quoting Sir Isaac Newton.)