Stoke’s Law

Introduction

The law, initially proposed by British physicist Sir Stokes in the year 1851,It is determined by taking the forces into account that are acting on a specific particle, as it sinks down in a liquid column under the effect of gravity. In Stoke’s law, the drag force F acting upward in opposition to the fall is equal to 6πrηv, where r is the radius of the sphere, η is the viscosity of the liquid, and v is the velocity of fall.

Stokes’ law is used in a lot of circumstances, most notably in the settling of sediments in fresh water and the determination of fluid viscosity. However, because its applicability is restricted to situations in which the particle’s motion does not induce turbulence in the fluid, different changes have been proposed.

Stoke’s Law Definition

Stoke’s Law is an equation that expresses the settling velocities of tiny spherical particles in a fluid medium.

In short, Stokes law addresses the active force applied to a body when it is dropped into a material. The falling body’s velocity initially remains low due to the low viscous contact. When the spherical body sinks with its effective weight, it experiences acceleration, and the body’s velocity slowly rises.

The force that slows a sphere as it passes through a viscous fluid is proportional to the sphere’s velocity, radius, and fluid viscosity. Sir George G. Stokes, an English scientist, established the viscous drag force F as Stokes’ law. Stokes’ law has several uses, including sediment settlement in freshwater and calculating fluid viscosity.

The net force on the body is zero in this instance, and it achieves a set velocity known as terminal velocity.

Stoke’s Law Formula

Sir, Stoke gives a formula of force that is viscous drag force:

“F=6πηrv”

Where, F = Drag force, η = fluid viscosity, v = sphere velocity

Derivation

The viscous force exerted on a sphere is proportional to the following parameters:

The viscosity coefficient is η.

The diameter of the sphere is r.

The object’s velocity is v.

As a result, 

F ∝ ηx ry vz ⇒ F =k ηx ry vz 

The following equation may be expressed in dimensions as

[MLT-2]  = k [ML-1 T-1]x ×[ L]y × [LT-1]z

When we solve it, we obtain x=1, y=1, and z=1.

As a result, F=kηrv

The experimental value of k for a spherical body was found to be 6. The viscous force on a spherical mass falling through a liquid is thus given by the equation: 

F = 6 π η r v

What is Terminal Velocity?

Terminal velocity is the constant speed attained by an object falling freely through a gas or liquid. 

A typical terminal velocity for a skydiver who waits too long to deploy the parachute is roughly 150 miles (240 kilometres) per hour. 

Raindrops have a significantly lower terminal velocity, while a spray of tiny oil droplets has an even lower terminal velocity. When an item is dropped from rest, its speed increases until it achieves terminal velocity; when an object is pushed to go faster than its terminal velocity, it slows down to this constant velocity upon release.

The Terminal velocity is reached, when a moving object has a speed that is no longer increasing or decreasing, and hence the object’s acceleration (or deceleration) is zero.

At the velocity that is terminal velocity, the air resistance is equal to the weight of the falling object in magnitude. 

Because the two forces are oppositely applied, the overall force on the item is zero, and the object’s speed has become constant.

Application Stoke’s Law

Some real life applications of Stoke’s Law

• Stokes’ law is also applied in settling pits to separate drilling mud from desirable drilling material, such as limestone.
• Larger raindrops hurt more to humans than tiny ones.
• A guy falling with the help of a parachute has constant terminal velocity.
• In oil refineries and petrochemical factories, for example, an API oil-water separator is used to separate water from oil.
• The floatation of clouds

Conclusion

Stoke’s Law combines known parameters of a particle and a fluid to calculate a particle’s velocity when its propelling force is exactly equal to the resistance of the fluid’s viscosity. Gravity is the most often used force, however it may be anything. When the requirements for the validity of Stoke’s Law are not satisfied when the particle is very big or moving quickly, causing the flow of fluid around the particle to be turbulent rather than smooth, Newton’s Resistance Law takes over. Moreover there are various real life applications of Stoke’s law that can be seen in real life which are already discussed in this article. Hope this article will help you in your academics.