Young–Laplace equation

describing pressure difference over an interface in fluid mechanics

In physics, the Young–Laplace equation (/ləˈplɑːs/) is a nonlinear partial differential equation that describes the capillary pressure difference across the interface between two static fluids, such as water and air. This difference is due to the phenomenon of surface tension or wall tension. Wall tension can only be used for very thin walls. The Young–Laplace equation relates the pressure difference to the shape of the surface or wall. It is very important in the study of static capillary surfaces.

Surface tension with the pendant drop method.
Optical tensiometers use the Young-Laplace equation to determine liquid surface tension automatically based on pendant droplet shape.

In physiology it is known as Laplace's law. It is used to describe the pressure inside hollow organs.

The equation is named after Thomas Young, who developed the qualitative theory of surface tension in 1805, and Pierre-Simon Laplace who completed the mathematical description in the following year. It is sometimes also called the Young–Laplace–Gauss equation: Carl Friedrich Gauss unified the work of Young and Laplace in 1830. Gauss derived both the differential equation and boundary conditions using Johann Bernoulli's virtual work principles.[1]


  1. Robert Finn (1999). "Capillary Surface Interfaces" (PDF). AMS.