= Solution
<Viscosity> transfers <momentum> between adjacent fluid layers. A <Newtonian fluid> has <shear stress> proportional to <strain> rate: for simple shear, $\boxed{\tau_{xy}=\eta\,\partial u_x/\partial y}$. Thus parallel plates of <area> $A$, separation $d$ and relative <speed> $U$ require force magnitude $\eta AU/d$ in a steady linear profile.
For an incompressible isotropic <Newtonian fluid>,
$$
\sigma_{ij}=-p\delta_{ij}+\eta(\partial_i u_j+\partial_j u_i),\qquad
\rho\frac{D\mathbf u}{Dt}=-\nabla p+\eta\nabla^2\mathbf u+\rho\mathbf g
$$
for constant <viscosity>. With <strain-rate tensor> $e_{ij}$, the <viscous dissipation> rate per unit volume is $2\eta e_{ij}e_{ij}\geq0$. <Kinematic viscosity> $\nu=\eta/\rho$ is the <momentum> diffusivity: a disturbance spreads over distance of order $\sqrt{\nu t}$.
The <Reynolds number> $\rho UL/\eta$ compares inertial and viscous forces. Small <Reynolds number> supports a creeping-flow approximation, while large values permit thin viscous <boundary layers> and possible <turbulence>. It does not mean molecular <viscosity> has disappeared. Gas <viscosity> results from molecular <momentum> transport; a liquid's microscopic transport depends strongly on intermolecular interactions. Non-Newtonian materials require a more general constitutive law.
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