CERTAIN EXACT SOLUTIONS TO THE PROBLEM OF LIQUID FLOW IN PRISMATIC TUBES

The problems of diff erent sections of physics and mechanics share a mathematical model that is based on the Poisson equation with a constant right-hand side and a zero (constant) value of the sought function on the contour of a two-dimensional region. A set of exact solutions to the formulated problem is presented in the "plane" region of certain form to describe the following problems: flow of a liquid in the channel at small Reynolds numbers; motion of an ideal liquid during the rotation of the contour bounding the region; torsion of a rod; deflection of the membrane at the zero displacement on the boundary of the region; heating of the rod. The possibility to construct approximate solutions for certain cross sections of the channel, etc. by using these exact solutions is noted. Examples are given.
   
Author:  A. I. Moshinskii
Keywords:  velocity profi le, channel, dimensionality, opening of the wedge, cavern
Page:  224