In the common Equilibrium distribution Function, we do not see the term rho (density). But in dimensionless form of the distribution function (sometimes referred as the normalized Maxwell’s distribution function) it comes up.
Common form= (4pic^2)((m/2kTpi)^3/2)(exp(-m.c^2/2kTpi))
Normalized form= (rho/(2*pi/3))(exp(-3(c-u)^2/2))
(U=c-u, c=micro speed, u=fluid bulk speed)
Note that there are other types of normalized form. Does anybody know the mathematical procedure? I greatly appreciate it…