The simplest eddy-viscosity model is the mixing-length hypothesis proposed by Prandtl. Building on Boussinesq's idea of representing turbulent friction by analogy with the Newton's law of viscosity, Prandtl further treated turbulent transport as analogous to molecular transport and thus constructed a simple model for determining the eddy viscosity

The basic idea is: in a turbulent flow, small fluid parcels (eddies) are assumed to move discretely like gas molecules. These parcels exchange momentum with the surrounding fluid only after traveling an effective distance. The average of this effective distance is called the mixing length. According to the kinetic theory of gases, the kinematic viscosity of a gas can be written as $$ \nu = K\,\overline{c}\,\lambda $$ where $\overline{c}$ is the mean molecular speed, $\lambda$ is the mean free path, and $K$ is a constant.
As an example, for air at 1 standard atmosphere (atm) and $15^\circ\mathrm{C}$, $\overline{c}=340~\mathrm{m\,s^{-1}}$, $\lambda=7\times10^{-8}~\mathrm{m}$, taking $K=0.499$ \(\longrightarrow\) $\nu=1.2\times10^{-5}~\mathrm{m^2\,s^{-1}}$

For simple turbulent shear flow, the eddy viscosity coefficient can be expressed as $$ \nu_t = C\,v^{*}\,l $$ where $v^{*}$ is the scale of the normal-direction velocity fluctuation, $l$ is the mixing length, and $C$ is a constant