  The statistical nature of discrete fluid molecules with random thermal motion
so far has not been considered in mainstream fluid mechanics based on
Navier-Stokes equations, wherein fluids have been treated as a continuum
breaking into many macroscopically infinitely small (but microscopically large
enough) mass elements with their motion only characterized by center-of-mass
velocity. Here we provide a Statistical Mechanical approach to address fluid
dynamics by considering statistical velocity distribution of discrete molecules
within macroscopically infinitely small volume elements as well as their
center-of-mass velocity. Dynamics equations governing the evolution of physical
variables have been proposed, Green's functions have been obtained and linear
response theory has been applied to study physical situations with external
heat perturbation. It is found that the propagation of heat, center-of-mass
motion and sound are intrinsically integrated in Statistical fluid dynamics.
This work lays down the foundation for applications of Statistical fluid
mechanics.
