In fluid mechanics, added mass or virtual mass is the inertia added to a system because an accelerating or decelerating body must move (or deflect) some volume of surrounding fluid as it moves through it. Added mass is a common issue because the object and surrounding fluid cannot occupy the same physical space simultaneously. For simplicity this can be modeled as some volume of fluid moving with the object, though in reality "all" the fluid will be accelerated, to various degrees. The dimensionless added mass coefficient is the added mass divided by the displaced fluid mass – i.e. divided by the fluid density times the volume of the body. In general, the added mass is a second-order tensor, relating the fluid acceleration vector to the resulting force vector on the body. Background Friedrich Wilhelm Bessel proposed the concept of added mass in 1828 to describe the motion of a pendulum in a fluid. The period of such a pendulum increased relative to its period in a vacuum (even after accounting for buoyancy effects), indicating that the surrounding fluid increased the effective mass of the system. The concept of added mass is arguably the first example of renormalization in physics. The concept can also be thought of as a classical physics analogue of the quantum mechanical concept of quasiparticles. It is, however, not to be confused with relativistic mass increase. It is often erroneously stated that the added mass is determined by the momentum of the fluid. That this is not the case, it becomes clear when considering the case of the fluid in a large box, where the fluid momentum is exactly zero at every moment of time. The added mass is actually determined by the quasi-momentum: the added mass times the body acceleration is equal to the time derivative of the fluid quasi-momentum. Virtual mass force Unsteady forces due to a change of the relative velocity of a body submerged in a fluid can be divided into two parts: the virtual mass effect and the Basset force. 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 where bold symbols denote vectors, is the fluid flow velocity, is the spherical particle velocity, is the