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Stokes' Law (Settling Velocity) Calculator

Terminal velocity of a spherical particle falling through a fluid.

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Settling Velocity

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Overview

Stokes' Law defines the terminal velocity reached by a spherical particle as it settles through a stationary, viscous liquid under the influence of gravity. In geology, it is primarily used to calculate the settling rates of fine-grained particles, providing a mathematical link between grain size and depositional energy.

Symbols

Variables

v_s = Settling Velocity, ho_p = Particle Density, ho_f = Fluid Density, g = Gravity, R = Radius

Settling Velocity
Particle Density
Fluid Density
Gravity
Radius
Dynamic Viscosity

Apply it well

When To Use

When to use: This equation is valid for fine-grained particles like silt and clay where the Reynolds number is very low (less than 0.1). It assumes the particle is a perfect sphere, the fluid is homogeneous and still, and there is no interference from other nearby particles.

Why it matters: It allows geoscientists to determine how long it takes for specific sediment types to settle in bodies of water, which is crucial for interpreting paleoenvironments. It also aids in the design of settling basins for industrial water treatment and understanding the transport of atmospheric dust.

Avoid these traps

Common Mistakes

  • Using diameter instead of radius.
  • Forgetting the viscosity unit (Pa·s).

One free problem

Practice Problem

A quartz silt grain with a radius of 0.00001 m is settling in water at 20°C. Given the density of quartz is 2650 kg/m³, the density of water is 1000 kg/m³, and the dynamic viscosity of water is 0.001 Pa·s, calculate the terminal settling velocity.

Particle Density2650 kg/m³
Fluid Density1000 kg/m³
Gravity9.81 m/s²
Radius0.00001 m
Dynamic Viscosity0.001 Pa·s

Solve for:

Hint: Subtract the fluid density from the particle density first, then multiply by the constant 2/9.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Bird, R. Byron, Stewart, Warren E., Lightfoot, Edwin N. Transport Phenomena. John Wiley & Sons.
  2. Incropera, Frank P., DeWitt, David P., Bergman, Theodore L., Lavine, Adrienne S. Fundamentals of Heat and Mass Transfer. John Wiley & Sons.
  3. Wikipedia: Stokes' Law
  4. Britannica: Stokes' law
  5. Bird, R. Byron; Stewart, Warren E.; Lightfoot, Edwin N. (2007). Transport Phenomena (2nd ed.). John Wiley & Sons.
  6. Incropera, Frank P.; DeWitt, David P.; Bergman, Theodore L.; Lavine, Adrienne S. (2007). Fundamentals of Heat and Mass Transfer (6th ed.).
  7. Bird, R. Byron, Stewart, Warren E., and Lightfoot, Edwin N. Transport Phenomena. 2nd ed. John Wiley & Sons, 2002.
  8. Boggs, Sam. Principles of Sedimentology and Stratigraphy. 5th ed. Pearson Prentice Hall, 2012.