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Viscosity is internal friction in fluids, opposing relative motion between adjacent layers. Newton's law: $F = \eta A (dv/dy)$, where $\eta$ is dynamic viscosity (Pa s, dimensional formula [M L$^{-1}$ T$^{-1}$]) and $dv/dy$ is the velocity gradient. Temperature dependence: liquid viscosity decreases with temperature (weakening cohesive forces); gas viscosity increases (more molecular collisions).

Stokes' law gives the drag on a sphere: $F = 6\pi\eta rv$, valid for low Reynolds numbers ($Re < 1$). Terminal velocity occurs when drag + buoyancy = weight: $v_T = 2r^2(\rho_s - \rho_f)g/(9\eta)$. Critical scaling: $v_T \propto r^2$ — doubling the radius quadruples the terminal velocity.

Poiseuille's equation for pipe flow: $Q = \pi\Delta P r^4/(8\eta L)$. The $r^4$ dependence is dramatic — halving the pipe radius reduces flow by 93.75% (factor of 16). This explains why even small arterial blockages severely reduce blood flow. The velocity profile is parabolic with $v_{\max} = 2v_{\text{avg}}$.

The Reynolds number $Re = \rho vD/\eta$ determines flow regime: laminar ($Re < 2000$) or turbulent ($Re > 4000$).