Stokes' Law

Fluid Dynamics · 1851

Equation: F_d = 6π μ r v; terminal v = 2 (ρ_p − ρ_f) g r² / (9 μ)
Field: Fluid Dynamics
Named After: George Gabriel Stokes
Year: 1851

Symbols

F_d drag on a small sphere moving slowly through a fluid · μ dynamic viscosity · r sphere radius · v its speed · ρ_p, ρ_f particle and fluid density

Significance

For a small particle in slow flow, drag is proportional to speed, and a settling particle reaches a terminal velocity that goes as the square of its radius. That is why fine tailings take days to clear a pond and clays may never settle, why dust hangs in air, why sediment sorts itself by grain size, and how a flotation cell and a settling tank are sized. Valid while the Reynolds number stays below about one.

Requires

Archimedes' Principle Reynolds Number Sphere: Surface and Volume Newtonian Viscosity

Impacts

Tailings dam failure Riverine tailings disposal Dust and particulates Silicosis

Referenced by

equation

Archimedes' Principle Newtonian Viscosity Reynolds Number Sphere: Surface and Volume

impact

Dust and particulates Riverine tailings disposal Silicosis Tailings dam failure

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