Abstract: By studying the internal wall of columniform capillary, the liquid and gas in it, and regarding the surface of the liquid as the rotational surface, we deduce the free energy functional. When the free energy functional arrives maximum, the Euler equation turns to the Laplace formula of additional pressure, and we also derivate the Young＇s equation by use of the moving boundaries conditions. It is a necessary condition for the two functions at the extremum for free energy functional.

Key words: capillary phenomena, calculus of variations, Euler and Laplace equations, boundary conditions and Young＇s equation