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Stokes' law gives the viscous drag on a sphere of radius $r$ moving at velocity $v$ through a fluid of viscosity $\eta$: $F = 6\pi\eta rv$. This is valid for creeping flow (Reynolds number based on sphere diameter $< 1$).

Terminal velocity is reached when the net force on a falling sphere is zero: weight = buoyancy + drag. This gives $v_T = 2r^2(\rho_s - \rho_f)g/(9\eta)$. Key dependencies: $v_T \propto r^2$ (quadruples when radius doubles), $v_T \propto (\rho_s - \rho_f)$ (denser sphere relative to fluid falls faster), $v_T \propto 1/\eta$ (higher viscosity means lower terminal velocity).

The velocity-time graph shows initial acceleration (when drag is small) followed by an asymptotic approach to $v_T$. At the instant of release, acceleration is maximum: $a = g(1 - \rho_f/\rho_s)$. At terminal velocity, acceleration is zero.

Applications: sedimentation rate in blood tests, settling of dust particles, designing parachutes, and understanding raindrop sizes.