Formula Stokes friction Frictional force Dynamic viscosity Radius Velocity
$$F_{ \text R} ~=~ 6 \pi \, \eta \, r \, v$$ $$F_{ \text R} ~=~ 6 \pi \, \eta \, r \, v$$ $$\eta ~=~ \frac{ F_{\text R} }{ 6\pi \, r \, v }$$ $$r ~=~ \frac{ F_{\text R} }{ 6\pi \, \eta \, v }$$ $$v ~=~ \frac{ F_{\text R} }{ 6\pi \, \eta \, r }$$
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 \( \text{Pa} \, \text{s} \) Viscosity *eta* indicates how viscous a fluid or gas is in which the particle is located. The greater the viscosity, the more viscous is the fluid or gas.
Radius
\( r \) Unit \( \mathrm{m} \) Radius of the particle. In the formula, we assume that the particle is spherical.
Velocity
\( v \) 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.