Determination of Frequencies and Decrements of Oscillations of Viscous Liquid Which Partially Fills A Circular Horizontal Canal

摘要

Normal ascillations of viscous incompressible liquid partially filling a circular horizontal canal investigated. A condition of slipping with friction is considered on the solid wall. The problem decisions are built by determining stationary values of the quadratic functional. To realized the projection method in the case of a half-filled circular canal a special system of coordinate functions which exactly satisfy the equation and three of four boundary conditions has been built. The suggested procedure allowed determining some of first frequencies and decrements of oscillations with high accuracy.