Added mass is a common issue because the object and surrounding fluid cannot occupy the same physical space simultaneously.
[1] Friedrich Wilhelm Bessel proposed the concept of added mass in 1828 to describe the motion of a pendulum in a fluid.
The origin of the force is that the fluid will gain kinetic energy at the expense of the work done by an accelerating submerged body.
It can be shown that the virtual mass force, for a spherical particle submerged in an inviscid, incompressible fluid is[6] where bold symbols denote vectors,
Moving the derivative of the particle velocity from the right hand side of the equation to the left we get so the particle is accelerated as if it had an added mass of half the fluid it displaces, and there is also an additional force contribution on the right hand side due to acceleration of the fluid.
In ship design, the energy required to accelerate the added mass must be taken into account when performing a sea keeping analysis.
This situation can occur, for instance, when the sinking body has a large flat surface with its normal vector pointed in the direction of motion (downward).
A substantial amount of kinetic energy is released when such an object is abruptly decelerated (e.g., due to an impact with the seabed).
In the offshore industry hydrodynamic added mass of different geometries are the subject of considerable investigation.
These studies typically are required as input to subsea dropped object risk assessments (studies focused on quantifying risk of dropped object impacts to subsea infrastructure).
As hydrodynamic added mass can make up a significant proportion of a sinking object's total mass at the instant of impact, it significantly influences the design resistance considered for subsea protection structures.
Proximity to a boundary (or another object) can influence the quantity of hydrodynamic added mass.
This means that added mass depends on both the object geometry and its proximity to a boundary.
The hydrodynamic added mass associated with a freely sinking object near a boundary is similar to that of a floating body.
In general, hydrodynamic added mass increases as the distance between a boundary and a body decreases.
This characteristic is important when planning subsea installations or predicting the motion of a floating body in shallow water conditions.
In aircraft (other than lighter-than-air balloons and blimps), the added mass is not usually taken into account because the density of the air is so small.
This added mass must e.g. be taken into account when designing the drive systems for these steel structures.