Added mass of a pair of discs

Abstract

Irrotational flow of inviscid incompressible fluid around a pair of coaxial discs of zero thickness, moving along their common axis, is considered. The added mass of an accelerating disc is modified by the presence of a second, coaxial disc. It is reduced if both discs accelerate equally in the same direction along their common axis and increased if their accelerations are equal in magnitude but in opposite directions. Other accelerations can be treated as linear combinations of these two cases. Analytic predictions are obtained when the disc separation 2z0 is large compared with the disc radius a and also when the discs are close (z0≪a). Results for intermediate separations are obtained as numerical solutions of a pair of dual integral equations.