Added Mass in a Model of a Viscous Incompressible Fluid

Abstract

It is proved that, with the same instantaneous distribution of the flow velocity of a viscous incompressible fluid, the forces acting on a body moving with acceleration and the forces acting on the body moving with constant velocity differ in the vector that is equal to the tensor of added masses multiplied by the acceleration vector. The tensor of added masses coincides with the tensor calculated for potential flows with the same geometry of the body and the surrounding surfaces and does not depend either on viscosity or on the distribution of vorticity in the flow space while the force corresponding to the motion with constant velocity depends on the motion prehistory.