# Stoke’s Law and Terminal Velocity | Definition, Formula – Hydrodynamics

Stoke’s Law Definition in Physics:
Stokes Law, named after George Gabriel Stokes, describes the relationship between the frictional force of a sphere moving in a liquid and other quantities. If a sphere or a body moves through a fluid, a friction force must be overcome.

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## Stoke’s Law and Terminal Velocity | Definition, Formula – Hydrodynamics

Stoke’s Law Formula:
When a small spherical body falls in a liquid column with terminal velocity, then viscous force acting on it is

F = 6πηrv

where,
r = radius of the body,
v = terminal velocity and
η = coefficient of viscosity. This is called Stoke’s law.

Terminal Velocity Definition:
When a small spherical body falls in a long liquid column, then after sometime it falls with a constant velocity, called terminal velocity.

Terminal Velocity Formula in terms of Viscosity:

Terminal velocity, v = $$\frac{2}{9} \frac{r^{2}(\rho-\sigma) g}{\eta}$$

where,
ρ = density of body,
a = density of liquid,
η = coefficient of viscosity of liquid and
g = acceleration due to gravity.

(i) If ρ > σ, the body falls downwards.
(ii) If ρ < σ, the body moves upwards with the constant velocity.
(iii) If ρ << ρ, v = $$\frac{2 r^{2} \rho g}{9 \eta}$$

• Terminal velocity depends on the radius of the sphere in such a way that, if radius becomes n times, then terminal velocity will become n² times.
• Terminal velocity-Time/distance graph

### Importance of Stoke’s Law

(i) This law is used in the determination of electronic charge by Millikan in his oil drop experiment.
(ii) This law helps a man coming down with the help of parachute.
(iii) This law accounts for the formation of clouds.

Hydrodynamics:
In physics, hydrodynamics of fluid dynamics explains the mechanism of fluid such as flow of liquids and gases. It has a wide range of applications such as evaluating forces and momentum on aircraft, prediction of weather, etc.