- #1

albertrichardf

- 165

- 11

Suppose you have an incompressible fluid in a column of infinite height and area and that is in a vacuum. The formula for the net pressure at any point is hpg, where p is the density and h the height.

The formula comes from considering that at h = 0, the net pressure is zero, but that at h = h the pressure there must not only balance the exerted by the random collisions of the molecules, but also that of the weight of all the water above. The pressure from random collisions is balanced because throughout the fluids the molecules move in the same way, but what force balances the pressure from gravity?

I would think it to be a reaction force to gravity, like the normal force when you place an object on a table. In the same sense, the weight of the fluid above is balanced by the normal force of the fluid below, and thus there is a pressure difference due to the normal force exerted by the fluid, but I'm not sure if this is correct. If it is not, then from where does the difference in pressures arise from? I know the force is there because the fluid is stationary, but what causes this force?

Assuming the above is correct, then I have problems seeing the buoyant force.

In most derivations that I have seen, the buoyant force arises due to the difference in pressure in the fluid below and above the object submerged. If the object has volume V, then the buoyant force is pVg, where p is the density of the fluid.

But these derivations seem to neglect the reaction force to the weight of the object. The fluid below the submerged object should feel a force due to the pressure of the fluid above it, and the weight of the object submerged. But in that case, it would exert a force by Newton's third law which would be equal to the weight of the object plus the weight of the fluid above it. This is akin to how I suppose the fluid exerts a reaction force to the weight of the fluid above to balance it. In the derivations, the reaction force to the fluid does not change despite the change in weight on the fluid below. So I must be missing something, but what?

Thanks for answers