A fluid contains an enormous number of molecules, but ordinary fluid mechanics does not track them individually. Instead it keeps a much smaller set of macroscopic fields such as density, pressure, temperature and velocity.

This transition is an example of model reduction: retain the information needed at the scale of interest and discard microscopic detail that is not resolved directly.

Microscopic description

At a molecular level, particles have positions and velocities and interact through collisions and intermolecular forces. Even a tiny macroscopic volume contains far too many particles for ordinary engineering calculations to follow individually.

Statistical description

Kinetic theory describes collections of particles statistically. Macroscopic quantities emerge from averages over many microscopic degrees of freedom.

For example, bulk flow velocity represents an average molecular motion, while temperature is related to random microscopic kinetic motion around that average.

Continuum fields

When the averaging scale is large compared with molecular distances but small compared with the flow features of interest, the fluid can be represented by continuous fields:

$$\rho(\mathbf r,t),\qquad \mathbf v(\mathbf r,t),\qquad p(\mathbf r,t).$$

The continuum equations do not claim that matter is literally continuous. They are an effective description at a chosen scale.