Stokes drag is the viscous resistance on a slowly moving sphere.
Difficulty
Intermediate
Read time
4 min
Prerequisites
Consistent SI units, algebra, and the physical assumptions listed below
Source
Teng-Jui Lin — Equation SheetsAdapted from Teng-Jui Lin, Equation Sheets — Mechanical Engineering, under CC BY 4.0.
Adapted notation and added original explanations, variables, assumptions, applications, and a worked example. Converted the no-slip spherical friction coefficient to force using F_D = f v.
Stokes drag is the viscous resistance on a slowly moving sphere. It is linear in relative speed, unlike the approximately quadratic drag common at larger Reynolds numbers.
| Symbol | Meaning | Units |
|---|---|---|
| Drag-force magnitude | ||
| Fluid dynamic viscosity | ||
| Sphere radius | ||
| Relative speed between sphere and far-field fluid |
Estimate resistance on a small slowly moving sphere.
Combine drag with buoyancy-corrected weight at terminal speed.
A sphere of radius 1.0 mm moves at 0.010 m/s through a liquid with viscosity 0.50 Pa·s and density 1000 kg/m³. Find drag; Re_p = 0.04 is small.
Adapted from Teng-Jui Lin, Equation Sheets — Mechanical Engineering, under CC BY 4.0.
Adapted notation and added original explanations, variables, assumptions, applications, and a worked example. Converted the no-slip spherical friction coefficient to force using F_D = f v.
Assumptions
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