| Abstract: | In 1–5] boundary-layer methods were used to solve problems concerned with the equilibrium and motion of a liquid with surface tension in a strong gravitational field (for large Bond numbers Bo). In the present paper we apply these methods to problems involving the equilibrium shape of a uniformly rotating liquid, contained in a cylindrical container of arbitrary cross section or in a container which is a surface of revolution about the z axis. Both of these problems reduce to the asymptotic integration of an equation with a small parameter involving a quasilinear elliptic operator with a nonlinear boundary condition. In the second case, owing to radial symmetry, the equation for the problem goes over into an ordinary equation; however, the wetted boundary is not known beforehand. This boundary, together with the equilibrium shape, is also determined asymptotically.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 3–12, November–December, 1973.The authors thank L. A. Slobozhanin for his help in the preparation of this paper. |
