• id: JME-09-N11
• title: Stokes' Law and Terminal Velocity
• tags: stokes, terminal-velocity, sphere

Stokes' Law: The viscous drag on a sphere of radius $r$ moving at velocity $v$ through a fluid of viscosity $\eta$ is $F = 6\pi\eta r v$. Valid for low Reynolds number (creeping flow, $Re < 1$). Terminal velocity: when drag + buoyancy = weight: $6\pi\eta r v_T + \frac{4}{3}\pi r^3 \rho_f g = \frac{4}{3}\pi r^3 \rho_s g$. Solving:$v_T = \frac{2r^2(\rho_s - \rho_f)g}{9\eta}$. Key scaling:$v_T \propto r^2$— doubling the radius quadruples the terminal velocity. Applications: raindrops reach terminal velocity, sedimentation in blood tests, fog droplets.$