Stoke's Law

Statement: Stokes' Law describes the force of viscosity exerted on a spherical object as it moves through a fluid. The viscous drag on a spherical body of radius r, moving with velocity v, in a medium of viscosity η is given by:

Key Points:

• The negative sign in F = −ηA\[\frac {dv}{dx}\] shows that viscous force opposes the direction of motion.
• At terminal velocity, upward viscous force + buoyant force = weight of the body.
• Terminal velocity formula derived from Stokes' Law:
  v₀ = \[\frac{2gr^2(\rho-\sigma)}{9\eta}\]
• Terminal velocity is proportional to r² — larger spheres fall faster.
• The coefficient of viscosity η has dimensional formula [ML⁻¹T⁻¹].
• SI unit of viscosity: Ns/m² (or Pa·s); CGS unit: dyne·s/cm² = poise.