Archimedes' Principle

When an object is submerged in a fluid, the fluid exerts pressure on all surfaces. Since pressure increases with depth ($P = P_0 + \rho g h$), the bottom of the object experiences greater pressure than the top. This pressure difference produces a net upward force called the buoyant force $F_B$.

Consider a submerged object of height $\ell$ with horizontal top and bottom surfaces of area $A$. Let the top surface be at depth $h_1$ and the bottom at depth $h_2 = h_1 + \ell$. The pressures are:

The upward force from below exceeds the downward force from above. The net buoyant force is:

The product $\ell A$ equals the volume $V$ of fluid displaced by the object.