Microcomputer-Based Laboratory for Archimedes' Principle and Density of Liquids

Archimedes' principle is one of the fundamental themes of the mechanics of fluids in high school; it is described in detail in any introductory physics textbook1 and it asserts that “a body immersed, or partially immersed, in a fluid receives an upward force equal to the weight of the fluid it displaces.” In mathematical terms, Fup = ρgVx, where ρ is the fluid density, g the free-fall acceleration, and Vx the volume of the immersed portion of the body. In a partially immersed body, the fluid exerts pressure on all surfaces of the body, laterally and on the bottom [Fig. 1(a)]. Notice that the forces on the sides cancel by symmetry and the net effect of the fluid pressure is an upward buoyant force. Likewise, if the body is totally immersed [Fig. 1(b)], the fluid also exerts pressure on the top of the body, but since the pressure on the bottom will be greater than on the top (pressure increases linearly with depth in a fluid of uniform density), the result is a net upward buoyant force.