What is Fluid particle; the continuum hypothesis?

A fluid particle is a volume of fluid small enough to be treated as a point on the scale of the flow, yet large enough to contain a huge number of molecules, so that its density $\rho$, pressure $P$, temperature $T$ and mean velocity $\vect v$ are well-defined averages (the mesoscopic scale, typically a micrometre). The continuum hypothesis assumes such a scale exists: the mean free path $\ell$ of the molecules must be much smaller than the scale $L$ of the flow, $\ell/L \ll 1$. In air at atmospheric pressure $\ell \approx 70\,\mathrm{nm}$; in a liquid $\ell$ is the molecular size. The fluid is then described by fields $\rho(M, t)$, $P(M, t)$, $\vect v(M, t)$ defined at every point.