Stokes' Law Calculator

When to Use Each Variable

• Solve for Drag Force — when you know the viscosity, sphere radius, and velocity, e.g., calculating resistance on a falling-ball viscometer sphere.
• Solve for Viscosity (Drag) — when you know drag force, radius, and velocity, e.g., measuring fluid viscosity with a falling-ball or rising-bubble apparatus.
• Solve for Radius (Drag) — when you know drag force, viscosity, and velocity, e.g., estimating particle size from measured drag in a sedimentation experiment.
• Solve for Terminal Velocity — when you know particle and fluid properties, e.g., predicting settling rates for sediment particles in a clarifier.
• Solve for Particle Diameter — when you know terminal velocity and fluid properties, e.g., determining the size of particles that settle at a measured rate.
• Solve for Viscosity (Terminal) — when you know particle properties and terminal velocity, e.g., back-calculating viscosity from sedimentation data.

Key Concepts

Stokes' Law describes the drag force on a small sphere moving slowly through a viscous fluid, valid when the Reynolds number is below 1 (creeping flow regime). Drag is directly proportional to velocity, viscosity, and sphere radius — doubling any one doubles the drag. Terminal velocity occurs when drag equals the net gravitational force on the particle, resulting in constant settling speed. This is the foundation for sedimentation analysis, particle sizing, and viscometry.

Applications

• Sedimentation analysis: determining soil particle size distribution by measuring settling times in a hydrometer test
• Viscometry: measuring fluid viscosity using falling-ball and rising-bubble viscometers
• Air quality: modeling the settling and suspension of aerosol particles, fog droplets, and dust
• Wastewater treatment: designing clarifiers and settling tanks by predicting particle settling velocities
• Pharmaceutical manufacturing: controlling particle size in suspension formulations for consistent drug delivery

Common Mistakes

• Applying Stokes' Law above Re = 1 — at higher Reynolds numbers, inertial effects become significant and the linear drag relationship breaks down
• Using diameter instead of radius in the drag equation — Fd = 6 pi mu r v uses radius, not diameter
• Forgetting the density difference in terminal velocity — buoyancy reduces the effective gravitational force, and omitting fluid density overestimates settling speed
• Ignoring particle shape — Stokes' Law applies to perfect spheres; irregular particles require correction factors