When deriving the hydrostatic equilibrium for a static fluid, it is said that the net force on a fluid element dV of the fluid must be 0 because it is at rest (on the average, of course). There is a downwards force acting on the fluid element due to the weight of the water above it, and also there is another downwards force due to the weight of the fluid element itself. Therefore, in order for there to be equilibrium, there must be an upwards force on the fluid element that exactly equals the total downwards force. However, I am very confused about the origin of this force.

An upwards force is mandatory for there to be equilibrium, there's no doubt about that. However, what is the origin of this upwards force?

For the downwards force for example, the origin is reasonable, it is due to the weight. But for the upwards force, is the reason due to "collisions" of the liquid molecules below on the fluid element or what? I've read that this upwards force is caused because the pressure below the fluid element is greater than the pressure acting on top of the fluid element, but I am still not able to get why the fact that there is more pressure justifies that there is an upwards force. Also, the reason for the buoyant force is this difference in pressures, if I am not wrong, but then what is the reason for the buoyant force?. Also, another way to think about this situation is that the upwards force is due to the normal force, just like a solid object standing on the earth has a normal force, but this doesn't explain too much about the origin of the upward force. The normal force on a solid object on earth is due to the electric repulsion of the molecules of the block and the molecules of the ground of the earth, since they are being "pushed together" due to the weight of the solid object, and this causes the repulsion. I wonder if this is the same reason for the upwards force in a static fluid scenario, but I'm not sure.

I hope that someone can help clear my confusion, I would appreciate it a lot.

• The force exerted on a part of the fluid by the surrounding fluid is due to the fluid's pressure. Microscopically, the pressure is due to electromagnetic forces exerted between particles in the fluid.
– d_b
Feb 13, 2022 at 22:04