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How It Works
Stokes' Law gives the drag force on a small sphere moving slowly through a viscous fluid: Fd = 6πμrv. It applies when the Reynolds number is low (Re < 1), meaning viscous forces dominate over inertial forces. The drag is proportional to velocity, viscosity, and sphere radius.
The terminal velocity equation Vt = gd²(ρp−ρm)/(18μ) calculates the constant speed a spherical particle reaches when drag force balances the net gravitational force. This is widely used in sedimentation analysis and particle settling studies.
Example Problem
A 0.5 mm radius sphere falls through oil (μ = 0.1 Pa·s) at 0.01 m/s. What is the drag force?
- Fd = 6π × 0.1 × 0.0005 × 0.01
- Fd ≈ 9.42 × 10−&sup6; N
Frequently Asked Questions
When does Stokes' Law apply?
Stokes' Law is valid at low Reynolds numbers (Re < 1), which means small, slow-moving spheres in viscous fluids. Examples include sediment settling, fog droplets, and blood cells.
What is terminal velocity in Stokes flow?
Terminal velocity occurs when drag equals the net gravitational force on the sphere. At that point the sphere falls at constant speed. For a dense sphere in a light fluid, Vt = gd²(ρp−ρm)/(18μ).
How is Stokes' Law used in practice?
It is used to measure fluid viscosity (falling-ball viscometer), determine particle size in sedimentation analysis, and model aerosol behavior in air quality studies.
Related Calculators
- Friction Calculator — calculate contact friction between surfaces.
- Density Calculator — find fluid or particle density.
- Force Equation Calculator — general force calculations.
- Reynolds Number Calculator — verify laminar flow conditions required for Stokes law.
- Viscosity Converter — convert dynamic viscosity units used in drag calculations.
Reference: Lindeburg, Michael R. 1992. Engineer In Training Reference Manual. Professional Publication, Inc. 8th Edition.