Archimedes’ principle with surface tension effects in undergraduate fluid mechanics

Abstract

The general physics of how objects float is only partly covered in most undergraduate fluid mechanics courses. Although Archimedes’ principle is a standard topic in fluid statics, the role of surface tension in floating is rarely discussed in detail. For example, very few undergraduate textbooks, if any, mention that the total buoyancy force on a floating object includes the weight of the fluid displaced by the meniscus. This leaves engineering students without an understanding of a wide range of phenomena that occur at a low Bond number (the ratio of buoyancy to interfacial tension forces), such as how heavier-than-water objects can float at a gas-liquid interface. This article makes a case for teaching a more unified version of Archimedes’ principle, which combines the effects of surface tension and hydrostatic pressure in calculating the total buoyancy on floating objects. Sample problems at the undergraduate level and two classroom demonstrations are described that reinforce the basic science concepts.