A Fresh Look at the Young-Laplace Equation and Its Many Applications in Hydrostatics

Abstract

The Young-Laplace (Y-L) equation relates the pressure difference across the interface of two fluids (such as air and water) to the curvature of the interface. The pressure rises on crossing a convex interface such as a rain drop and falls on crossing a concave interface such as the meniscus of water in a glass capillary. The relation between surface geometry and pressure difference across the interface provides the key concept in understanding a large collection of phenomena in hydrostatics. Of the many phenomena in hydrostatics that can be explained readily by the application of the Y-L equation, we consider the ones that are of particular interest in the introductory physics courses. These include the differential pressure within soap bubbles and liquid droplets, the rise and fall of liquids in capillaries, and the depth of liquid spills.