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 mass density of the fluid (continuous phase),  is the volume of the particle, and D/Dt denotes the material derivative.
The origin of the notion "virtual mass" becomes evident when we take a look at the momentum equation for the particle.
where  is the sum of all other force terms on the particle, such as gravity, pressure gradient, drag, lift, Basset force, etc.
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.