I'm trying to work out the upward vertical force which will be generated (per linear m) when the prismatic form below is filled with a fluid, in order to counter it by applying a downward force equal or larger in magnitude.
As a rough indication of scale, H ≈ 1 m, a ≈ 0.1 m, b ≈ 0.5 H, making the slope close to 2:1.
I suspect I should use (Hρg) using the average depth (=H/2) and area of the slanted side to get the force acting on the slanted surface per linear m, then take this force as acting normal to the slanted surface and resolve its vertical component, and assume that's the only upward force generated on the prism. That would give a value of: (H/2)(ρg) . √(H2 + b2) . cos(tan-1(H/b)) = (Hb/2) . (ρg) (since cos(tan-1(H/b)) == b/√(H2 + b2) ) as the upward force to be countered per metre.
But while checking this, I've also seen calculations for dams and other submerged slanted surfaces using the centroid, and now I'm a bit unsure. Also hydrostatics was never my subject. Have I got this right in principle?
(The actual situation is that I'm casting a prismatic shape using a very dense low-viscosity fluid which sets after some time (imagine something similar to a very dense, very fluid, plaster of paris or cement, with a density ≈ 2700 kg/m^3). For practical reasons, while it's easy to clamp and brace the mould to counter the horizontal forces and any moments generated by the fluid before it sets, there's nothing available externally to hold/anchor the bottom of the mould to the floor or ground. So it has to be held down against uplift forces by adding equivalent weight on top. Most of the hydrostatic force *should* act horizontally, at a guess, but I need to be sure I've got enough weight on top when I start casting, or the fluid will just lift the mould off the ground and flow from under it ;-) )