# Stoke’s Law

## Stoke’s Law

When a body moves through a fluid it experiences a resistive force because the presence of the fluid. Every fluid has a property called viscosity, the resistance of a fluid to anybody moving through it. Thicker, more viscous materials resist more the movement of bodies through them than thinner, less viscous materials.

The viscosity of a material is described by it’s coefficient of viscosity ,Under conditions of low velocity and non-turbulent motion, the force experience by a sphere moving through a fluid is described by Stoke’s Law.

What is Stoke’s Law?

The force that retards a sphere moving through a viscous fluid is directly proportional to the velocity and the radius of the sphere and the viscosity of the fluid.

Mathematically:

F = 6πηrv; Where,

r = Radius of the Spherical body,

v = Velocity of the Spherical body.

Stoke’s Law is applicable only to laminar flow of liquids. It is not applicable to turbulent flow. Stoke’s Law gives the relationship between retarding force and velocity. When viscous force + buoyant force becomes equal to force due to gravity, the net force becomes zero. The sphere then descends with a constant terminal velocity.

$$6\pi \eta rv=\frac{4}{3}\pi {{r}^{3}}\left( \rho -\sigma \right)g$$;

Where,

ρ = Density of the liquid,

σ = Density of the spherical body,

Terminal velocity of a spherical body of density ρ and radius r moving through a liquid of density σ is:

$$v=\frac{2}{9}\frac{{{r}^{2}}\left( \rho -\sigma \right)g}{\eta }$$;

Where,

ρ = Density of the body,

σ = Density of the liquid,

η = Coefficient of viscosity of liquid,

g = Acceleration due to gravity.

Importance of Stoke’s Law:

• This law is used in the determination of electronic charge by Millikan in his oip drop experiment.
• This law helps a man coming down with the help of a parachute.
• This law account for the formation of clouds.