Formula: Stokes Friction Frictional force Viscosity Radius Velocity
$$F_{ \text R} ~=~ 6 \pi \, \eta \, r \, \class{blue}{v}$$
$$F_{ \text R} ~=~ 6 \pi \, \eta \, r \, \class{blue}{v}$$
$$\eta ~=~ \frac{ F_{\text R} }{ 6\pi \, r \, \class{blue}{v} }$$
$$r ~=~ \frac{ F_{\text R} }{ 6\pi \, \eta \, \class{blue}{v} }$$
$$\class{blue}{v} ~=~ \frac{ F_{\text R} }{ 6\pi \, \eta \, r }$$
Frictional force
$$ F_{\text R} $$ Unit $$ \mathrm{N} $$
The Stokes friction force decelerates the particle, i.e. it acts against its velocity. A requirement for the validity of this formula is that the size of the particle is greater than its mean free path. If this is not fulfilled, then the Cunningham correction should be used to get a more accurate result for friction force.
Dynamic viscosity
$$ \eta $$ Unit $$ \frac{\mathrm{kg} \cdot \mathrm{m}}{ \mathrm s } $$
Viscosity \( \eta \) (pronounced: Eta) is a property of a fluid (liquid or gas) and describes how difficult it is to move a body through this fluid.
| Liquid | Viscosity \( \eta \) |
|---|---|
| Olive oil | \( 108 \cdot 10^{-3} \, \frac{\mathrm{kg}}{ \mathrm{m}\cdot \mathrm{s} } \) |
| Honey | \( 10\,000 \cdot 10^{-3} \, \frac{\mathrm{kg}}{ \mathrm{m}\cdot \mathrm{s} } \) |
| Glycerin | \( 1500 \cdot 10^{-3} \, \frac{\mathrm{kg}}{ \mathrm{m}\cdot \mathrm{s} } \) |
| Water | \( 1.008 \cdot 10^{-3} \, \frac{\mathrm{kg}}{ \mathrm{m}\cdot \mathrm{s} } \) |
| Tar | \( 100\,000 \cdot 10^{-3} \, \frac{\mathrm{kg}}{ \mathrm{m}\cdot \mathrm{s} } \) |
Radius
$$ r $$ Unit $$ \mathrm{m} $$
Radius of the particle. In the formula, we assume that the particle is spherical.
Velocity
$$ \class{blue}{\boldsymbol v} $$ Unit $$ \frac{\mathrm m}{\mathrm s} $$
Constant velocity of the particle directed opposite to the frictional force. The velocity can be the falling velocity, which occurs during falling due to friction.