Laplace formula

The Laplace formula is a result in fluid mechanics that gives the surface pressure between two continuous media. The surface of separation is really a transitional layer, but it is so thin that in classical mechanics it can be considered a dividing surface between the two media.

Definition

Consider two continuous media (top and bottom) whose surface of separation undergoes a small displacement. If $r_t$ and $r_b$ are the principal radii of curvature of the surface in some sample region, then the difference of pressures is

$\Delta P = \alpha\left(\frac{1}{r_t}+\frac{1}{r_b}\right)$

where $\alpha$ is the surface tension coefficient.

See also

• Fluid dynamics
• Young–Laplace equation
• Surface tension

References

• Landau, L.D. and Lifschitz, E.M. Fluid Mechanics. Oxford : Butterworth-Heinemann, 1987.
• "Film notes for surface tension in fluid mechanics" (PDF). Trefethen, Encyclopedia Britannica. 1969. Retrieved 2014-03-25.