Part 4/6:
To derive Archimedes' Principle, we can balance the forces acting on the object submerged in the fluid. The sum of forces in the vertical direction must equate to zero when at rest, meaning the buoyant force minus the weight must equal zero. This can be expressed mathematically, leading to the conclusion that the buoyant force is equal to the weight of the fluid displaced.
The formula can further be illustrated using the unit weight of fluid and its depth. By establishing the relationships of the pressures at both the top and bottom of the submerged object, one can derive an equation that simplifies to show the buoyant force as equal to the weight of the displaced water.