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Formulas

Stokes' Law (Viscous Drag)

Viscous drag force on a small sphere moving through a fluid.

Physics
Subject
Fluid Mechanics
Sub Subject
Viscosity
Chapter
Drag Force
Topic

Stokes' Law (Viscous Drag)

📊 advanced
$$F_d = 6\pi\eta r v$$
Viscous drag force on a small sphere moving through a fluid.
Variables & Units
$F_d$
Drag force
Unit: $\text{N}$
$\eta$
Dynamic viscosity
Unit: $\text{Pa·s}$
$r$
Sphere radius
Unit: $\text{m}$
$v$
Velocity relative to fluid
Unit: $\text{m/s}$
Key Information
📐 Derived From
Navier-Stokes equations for creeping flow
💡 Example
Water droplet $r=10^{-5}\,\text{m}$, $\eta=1\times10^{-3}\,\text{Pa·s}$, $v=0.01\,\text{m/s}$: $F_d = 6\pi(0.001)(10^{-5})(0.01) \approx 1.88\times10^{-9}\,\text{N}$.
🔧 Applications
Sedimentation, aerosol physics, viscometers
⚠️ Constraints
Low Reynolds number ($Re \ll 1$), incompressible fluid

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