Free motion of a solid body in the flow of a viscous incompressible fluid. Dissipation of the kinetic energy of a viscous fluid

Abstract

THE problem of the drag on solid bodies by the flow of a viscous incompressible fluid in an infinite cylindrical tube is solved numerically. It is observed that the drag process is optimal, in the sense of loss of kinetic energy by viscous friction, in a fairly large volume of the fluid containing the moving body, in the class of flows of a viscous fluid occurring in the motion of bodies along a tube at constant velocity. The problems of the drag in an infinite cylindrical tube by the flow of an incompr incompressible fluid possessing a Poiseuille velocity distribution at infinity, on a single particle and on two connected particles of cylindrical shape whose axes are the same as the axis of the tube, were solved numerically in [1–3]. For the composite body the interaction between the parts of the body occurring during the free motion of the solid body were studied. We recall briefly the formulation of the problem. We call the drag velocity or the velocity of the free motion of a solid body in a viscous fluid, that velocity for which the sum of the forces acting on the body is zero. The problem of the uniform motion of the body in the fluid relative to a laboratory coordinate system is non-stationary. On passing to an inertial coordinate system rigidly attached to the moving body, the motion with respect to this coordinate system becomes stationary.