Liquid Present In An Unsymmetrical Container Suppose there is an inverted container (like an unsymmetrical frustum, base area smaller than top area, and the sides make different angles with the vertical) kept on a smooth surface. If there is a liquid present inside the container, will the horizontal forces be balanced on the container?

• Force is pressure multiplied by area, and pressure is a function of depth only. Without seeing a diagram, my guess would be "no" the horizontal forces are not "balanced", but the sum of all the forces (or the integral of all the forces around the container, in a horizontal direction, if you prefer) would be balanced such that the container is not accelerated in any horizontal direction. – David White Apr 12 at 17:31
• But why would they be balanced. Some students try to relate it to real life, that we have never observed a liquid container accelerating, but then in real life there is friction acting on the container. Can you show me mathematically that the forces are balanced? I would be highly grateful. – Doctor Insult Apr 13 at 7:31
• Consider what happens if you reduce the width of the middle flat section, and reduce alpha so that side is almost vertical, and increase beta so that side is almost horizontal. – PM 2Ring Apr 13 at 7:35
• Mathematical proofs please. I don't find intuitions highly convincing. – Doctor Insult Apr 13 at 8:08
• @DoctorInsult, conservation of energy requires that the sum of the forces are balanced. If not, the container would experience a net force, and that net force would be able to do work with no input of energy into the system. And BTW, the added diagram is somewhat helpful. – David White Apr 13 at 15:54