On the added mass in a viscous incompressible fluid

Abstract

It is proved that at the same instantaneous distribution of the flow velocity of a viscous incompressible fluid, the forces acting on a body moving with acceleration differ from forces acting on the body moving with constant velocity by a vector, which is equal to the added masses tensor multiplied by the acceleration vector. The tensor of the added masses coincides with the tensor calculated for potential flows with the same geometry of the body and 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 history of movement.