A comprehensive overview of the Young-Laplace equation

Abstract The Young–Laplace equation relates the pressure difference across a fluid interface to its curvature and surface tension and plays a fundamental role in physical phenomena and engineering applications. This work aims to present a clear and pedagogically oriented exposition of the physical and mathematical foundations of the Young–Laplace equation. The approach combines a theoretical derivation with illustrative examples based on common physical situations. The results demonstrate how the equation quantitatively explains pressure variations in curved interfaces and clarifies the role of curvature in determining equilibrium configurations. These examples highlight the consistency between the mathematical formulation and observable phenomena. By systematically linking theory, derivation, and application, the work provides an accessible and comprehensive reference that supports the teaching and learning at undergraduate and graduate levels.