Stoke's Law: Definition, Formula, Derivation, Importance, Limitation &Application

Stoke's Law

Stoke's Law: Have you ever pondered why raindrops falling from such height do not harm us? The answer to this question is that because of Stokes's Law. This concept of Stoke's Law was formulated and named after scientist George Gabriel Stokes in the year 1851. This law gives the relationship between the frictional force of the sphere passing through a fluid medium. So in this article, we will discuss Stoke's Law in detail.

Stoke's Law is an equation that expresses the settling velocities of small spherical objects in a fluid medium. The law is established by taking into account the forces acting on an object or particle as it falls through a liquid column under the influence of gravity. The force that retards a sphere that passes through a viscous fluid medium is directly proportional to the velocity, radius and viscosity of the sphere. It can be written as-

F = 6πηrv

Stoke's Law Formula

Stoke came out with the concept to calculate the frictional force or drag force that is exerted upon spherical objects. The formula to calculate stoke's law is-

F = 6πηrv

Where, 

F indicates the frictional force or drag force

η indicates the viscosity of the liquid

r indicates the radius 

v indicates the velocity of the flow

Stoke's Law Derivation

As we know, The force that retards a sphere that passes through a viscous fluid medium is directly proportional to the velocity, radius and viscosity of the sphere. Mathematically, it can be written as-

F ∝ η^a r^b v^c

F = Kh η^a r^b v^c

Writing the dimension of the given parameters we get,

[MLT^-2] = [ML^–1T^–1]^a [L]^b [LT^-1]^c

[MLT^–2] = M^a ⋅ L^–a+b+c ⋅ T^–a–c… 

Equating the subscripts, we get,

a = 1

–a + b + c = 1

 a + c = 2

Equating the above equation we get, a=b=c=1

F = K * η^1 r^1 v^1 

F = K ηrv

Hence derived

Importance of Stoke’s Law

The following are the importance of Stoke’s Law:

• Millikan employs this concept in an oil-drop experiment to determine the electronic charge.
• The person falling from a great parachute.
• Cloud formation

Limitation of Stoke's Law

The limitation of Stoke's law are-

• Negative density difference in Stoke’s equation.
• A high content of dispersed solids.
• Dielectric Constant.
• Brownian movement.

Terminal Velocity

When an object falls through a fluid medium, it attains a constant velocity through a subsequent motion. This is because the net force on the body is due to gravity and fluid is zero. This constant velocity is termed terminal velocity. The formula for terminal velocity is-

 Vt = 2a² (ρ−σ) g / 9η

Where,

ρ and σ indicate sphere and fluid mass densities

Vt indicates the terminal velocity 

η indicates the viscosity of the liquid

Application of Stoke’s Law

Some of the applications of Stoke's law are-

• Velocity of Raindrops
• Parachute
• To calculate the charge of an electron(Millikan experiment)