= Solution
<Dynamic viscosity> measures resistance to a <velocity> gradient. In Newtonian simple shear, $\tau_{xy}=\eta\,\partial u_x/\partial y$; positive <viscosity> dissipates mechanical <energy> into <heat>. <Kinematic viscosity> is $\nu=\eta/\rho$. For an incompressible fluid of constant <viscosity>,
$$
\rho\left(\partial_t\mathbf u+\mathbf u\cdot\nabla\mathbf u\right)
=-\nabla p+\eta\nabla^2\mathbf u+\mathbf f.
$$
Scaling <velocity> by $U$ and length by $L$ gives the <Reynolds number> $\mathrm{Re}=\rho UL/\eta=UL/\nu$, the ratio of inertial to viscous terms. At small <Reynolds number>, creeping-flow approximations neglect inertia; at large <Reynolds number>, inertia dominates much of the bulk but <viscosity> can remain crucial in boundary layers. \b[A large <Reynolds number> permits instability and <turbulence>; it does not by itself specify a universal transition threshold.] Geometry and disturbances also matter.
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