Laplace formula

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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.


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.

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