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Stokes' Law (Viscous Drag)

๐Ÿ“Š 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: $\text{Paยทs}$
$r$
Sphere radius
Unit: $\text{m}$
$v$
Velocity relative to fluid
Unit: $\text{m/s}$
Key Information
๐Ÿ“ Derived From
Navier-Stokes equations for creeping flow
๐Ÿ’ก Example
Water droplet $r=10^{-5}\,\text{m}$, $\eta=1\times10^{-3}\,\text{Paยทs}$, $v=0.01\,\text{m/s}$: $F_d = 6\pi(0.001)(10^{-5})(0.01) \approx 1.88\times10^{-9}\,\text{N}$.
๐Ÿ”ง Applications
Sedimentation, aerosol physics, viscometers
โš ๏ธ Constraints
Low Reynolds number ($Re \ll 1$), incompressible fluid

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