The author derives an interesting generalized capillary equation under global phenomenologial assumptions without recourse to consideration of intermolecular attractions. This theory includes compressible liquids, which admit a pressure-density relation. In this case, the author arrives under the pressure-density assumption \(\rho=\rho_0+\chi(p-p_0)\), with \(p_0,\;\rho_0\) the pressure and density at the base \(\Omega\) of the (cylindrical) container, and \(\chi>0\), at the equation \[ \text{ div} {Du\over\sqrt{1+|Du|^2}}={\rho_0 g\over\sigma}\left(u-{\chi\sigma\over\sqrt{1+|Du|^2}}\right)+\lambda \] on \(\Omega\), where \(g\) is gravity acceleration, \(\sigma\) is surface tension, and \(\lambda=\)const. Set \(M=\rho_0/ \chi g\int_\Omega(1-e^{-\chi g u}) dx\), then a necessary condition for existence of solution of this equation which achieves a prescribed boundary contact angle is the condition \(\rho_0|\Omega|-\chi g M>0\). When \(\Omega\) is a disk, then existence and comparison results are shown for rotationally symmetric solutions. The derived equations, in particular for compressible liquids, are certainly of importance for practical engineering.