We are going to express Newton's Law as a function of linear momentum. We write Newton's Second Law,

\begin{equation} F_x=ma_x=m\frac{dv_x}{dt}=\frac{d(mv_x)}{dt}=\frac{dp_x}{dt} \end{equation}

Substituting into Newton's Law of viscosity:

\begin{equation} \frac{dp_x}{dt}=-\eta A\frac{dv_x}{dz} \end{equation}

$dp_x/dt$ (flow quantity of movement), represents the variation of the component and of the linear momentum of a layer located on one side inside the fluid, due to its interaction with the fluid on the other side. The molecular explanation of viscosity assumes momentum transport through planes perpendicular to the z axis.

Define the momentum flux per unit area and time: \begin{equation} J_z=\frac{1}{A}\frac{dp_x}{dt}=-\eta\frac{dv_x}{ dz} \end{equation}