I came across a question where i was asked to find the force exerted by the walls of a frustum shaped bucket on a liquid inside it . I found the force exerted by the liquid on the walls of the bucket by concepts of hydrostatic force and thought that by newton's third law both the forces will be equal and opposite . But the answer was totally different . I checked the solution in that simple force dynamics (newton's second law) was used considering the weight of the liquid , the normal force by the floor of the bucket, the atmospheric pressure and the force by the walls. Then since the liquid was at equilibrium all the forces were vetorially equated with each other . I am convinced with this solution but i also don't see any problem with my approach . So how should it be ?
I'm guessing that your problem lies in your determination of the force exerted on the slanted walls. Pressure always acts perpendicular to a surface, so this perpendicular pressure force must be resolved into horizontal and vertical components. You can then integrate that over the slanted walls (taking into account the hydrostatic changes in pressure with depth) to determine both the horizontal- and the vertical forces on the walls.