Question

Define stokes law and also write it's condition.

Answer 1

In 1851, George Gabriel Stokes derived an expression, now known as Stokes' law, for the frictional force – also called drag force – exerted on spherical objects with very small Reynolds numbers in a viscous fluid.[1] Stokes' law is derived by solving the Stokes flow limit for small Reynolds numbers of the Navier–Stokes equations.The force of viscosity on a small sphere moving through a viscous fluid is given by:[3]

{\displaystyle F_{d}=6\pi \,\eta \,R\,v\,}

where:

Fd is the frictional force – known as Stokes' drag – acting on the interface between the fluid and the particle

η is the dynamic viscosity (some authors use the symbol μ)

R is the radius of the spherical object

v is the flow velocity relative to the object.

In SI units, Fd is given in newtons (= kg m s−2), η in Pa·s (= kg m−1 s−1), R in meters, and v in m/s.

Stokes' law makes the following assumptions for the behavior of a particle in a fluid:

Laminar flow

Spherical particles

Homogeneous (uniform in composition) material

Smooth surfaces

Particles do not interfere with each other.

Note that for molecules Stokes' law is used to define their Stokes radius.

The CGS unit of kinematic viscosity was named "stokes" after his work.