Added mass

Added mass is the effective inertia contributed by fluid accelerated together with an immersed body.

Table of contents
- Added mass of a sphere Added mass
  - Acceleration of a freely falling sphere with added mass Added mass of a sphere

Added mass of a sphere

A sphere of volume

V

translating through unbounded inviscid incompressible fluid has fluid kinetic energy

K_{f} = \frac{1}{2} (\frac{ρ V}{2}) U^{2} .

Its added mass is therefore one half of the displaced fluid mass.

Acceleration of a freely falling sphere with added mass

A sphere of density

ρ_{s}

falling in inviscid fluid of density

ρ

has effective inertia

(ρ_{s} + ρ /2) V

and net weight

(ρ_{s} - ρ) V g

. Hence

\dot{U} = \frac{ρ _{s} - ρ}{ρ _{s} + ρ /2} g .

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