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.
Highlights
Determining whether an object floats or sinks in a liquid is arguably one of the most fundamental calculations in fluid statics
This analysis is accurate for fully submerged objects and floating objects at high Bond number, where the Bond number characterizes the relative importance of the buoyancy force to the surface tension force: Bo
A review of introductory fluid mechanics textbooks reveals that the analyses presented of the role of surface tension in floating are limited
Summary
Determining whether an object floats or sinks in a liquid is arguably one of the most fundamental calculations in fluid statics. The buoyancy force analysis in introductory fluid mechanics textbooks is based on the traditional Archimedes’ principle, which only accounts for the hydrostatic pressure on an object. This analysis is accurate for fully submerged objects and floating objects at high Bond number, where the Bond number characterizes the relative importance of the buoyancy force to the surface tension force: Bo. In Equation (1), σ is the surface tension, Δρ is the density difference between the liquid and gas phases, g is the gravitational acceleration and R is the characteristic length scale of the floating object. The total restoring force is the sum of the weight of the liquid displaced by the object and the meniscus We discuss how this generalized theory considers the effects of both surface tension and buoyancy,. Some limitations and anticipated difficulties in teaching this topic at the undergraduate level are discussed
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