addedmass

Added mass, also known as virtual mass, is the inertia that a body appears to have when accelerating through a fluid due to the need to accelerate some volume of surrounding fluid along with the body. It is not a real material mass of the body, but an inertial reaction arising from the fluid, and it can be described within potential-flow theory or more generally within hydrodynamics.

When a rigid body moves with velocity U in an incompressible, inviscid, unbounded fluid, the hydrodynamic force required to accelerate the body includes a contribution from the added mass: F = M_a dU/dt, where M_a is the added-mass tensor that depends on geometry, fluid density, and the direction of motion. The total kinetic energy equals (1/2) U^T (M_body + M_a) U, where M_body is the body's actual mass.

For simple shapes in an infinite fluid, closed-form added-mass expressions exist. For a solid sphere of radius a in a stationary fluid, M_a = (1/2) ρ V = (2/3) π ρ a^3. For a long circular cylinder of radius a moving along its axis with fluid occupying the exterior, the added mass per unit length is M_a/L = ρ π a^2. In general, M_a is a symmetric tensor, so the effective added mass depends on the direction of motion relative to the body.

In real fluids, viscosity and wave radiation modify these results, and added mass can become frequency-dependent or include damping terms. Nevertheless, added mass is a central concept in ship hydrodynamics, underwater vehicle dynamics, and offshore technology, where rapid accelerations can produce substantial transient forces due to fluid inertia.