Stokes' Law Calculator

Stokes' law describes the frictional drag force—also known as viscous force—exerted on spherical objects with very small Reynolds numbers in a continuous viscous fluid. The foundational equation for calculating terminal velocity (v) is: v = [g × d² × (ρ_p - ρ_m)] / (18 × μ), where 'g' is acceleration due to gravity, 'd' is the particle diameter, 'ρ_p' is the mass density of the particle, 'ρ_m' is the mass density of the fluid medium, and 'μ' is the dynamic viscosity of the fluid.

Let us calculate the terminal velocity of a small spherical particle dropping through a fluid. Assume the particle diameter (d) is 0.002 meters, particle density (ρ_p) is 2500 kg/m³, fluid density (ρ_m) is 1000 kg/m³, acceleration due to gravity (g) is 9.81 m/s², and dynamic viscosity (μ) is 0.89 Pa·s. First, find the density difference: 2500 - 1000 = 1500 kg/m³. Next, square the diameter: (0.002)² = 0.000004 m². Multiply g, d², and the density difference: 9.81 × 0.000004 × 1500 = 0.05886. Finally, divide by 18 times the viscosity (18 × 0.89 = 16.02), resulting in a terminal velocity of approximately 0.00367 m/s.

Stokes' law assumes that the falling particle is rigid, perfectly spherical, and smooth. It also requires the surrounding fluid to be infinite in extent and uniform in composition. Most importantly, ensure your Reynolds number remains well below 0.5; otherwise, turbulent drag will invalidate the laminar assumptions of this calculation.