Archimedes' Principle: The magnitude of the buoyant force on an object submerged in a fluid is equal to the weight of the fluid displaced by the submerged object. In equations:

buoyant force = F_b = weight of fluid displaced = m_{fluid displaced} g. But m_{fluid displaced} = density of fluid x volume of object = P_fluid V_object

Thus, we get:

F_b = P_fluid V_object g