Added mass fluid quasi-momentum. 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, formula_2 is the fluid flow velocity, formula_3 is the spherical particle velocity, formula_4 is the mass density
Derivation of the Navier–Stokes equations where it's assumed that all body forces are describable as gradients (for example it is true for gravity), and density has been divided so that viscosity becomes kinematic viscosity. The second vector calculus identity above states that the divergence of the curl of a vector field is zero. Since the (incompressible) mass continuity equation specifies the divergence of flow velocity being zero, we can replace the flow velocity with the curl of some vector formula_84 so that mass continuity is always satisfied: So, as long as flow velocity is represented through formula_86, mass continuity is unconditionally satisfied. With this new