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
Magnetic reconnection where formula_18 is the mass density of the plasma. Solving for the outflow velocity then gives where formula_20 is the Alfvén velocity. With the above relations, the dimensionless reconnection rate formula_21 can then be written in two forms, the first in terms of formula_22 using the result earlier derived from Ohm's law, the second in terms of formula_23 from the conservation of mass as Since the dimensionless Lundquist number formula_25 is given by the two different expressions of formula_21 are multiplied by each other and then square-rooted, giving a simple relation between the reconnection rate formula_21 and the Lundquist number