Stoke’s Law: Everything You Need to Know…!!!

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Have you ever wondered why rain falling from great heights doesn’t injure people because of gravity? Why Stoke’s Law easily explains this case. This is a beautiful illustration of a proportional retarding force. In 1851, George Gabriel Stokes created an equation for the drag force, commonly referred to as the frictional force.

The relationship between the frictional force of a sphere moving in a liquid and the other quantities are described by Stoke’s Law, which bears the name of the scientist George Gabriel Stokes. In order to move through a liquid, a body or sphere must overcome friction.

Let us look at what is Stoke’s Law and its importance and limitations in detail.


What is Stoke’s Law?

Small spherical particle settling velocities in a fluid media are expressed by Stoke’s Law. When establishing Stoke’s Law, consideration is given to the forces that are exerted on a specific particle as it descends down a liquid column under the effect of gravity.

A sphere’s velocity, radius, and fluid viscosity all have a direct relationship with the force that slows it down. The viscous drag force F was defined by English physicist Sir George G. Stokes as follows:

F = 6 × πηrv


F = frictional force

r = radius

v = velocity of the flow

η = viscosity of the liquid

As a crucial concept in Fluid Dynamics, Stoke’s law describes the active force that is delivered to a body when it is dropped into a substance. The low viscous contact causes the falling body’s initial velocity to remain low. The spherical body experiences acceleration and a steady increase in velocity when it sinks with its effective weight.

A sphere’s velocity, radius, and fluid viscosity all have a direct relationship with the force that slows it down. The vicious force F, as described by Sir George G. Stokes, has applications in a variety of fields, including determining the viscosity of fluids and sediment settlement in freshwater.

In this situation, a body experiences no net force and reaches its terminal velocity, which is a fixed speed. With the use of the definition, Stoke’s law was created, and the frictional force which is also known as Stoke’s drag is applied at the boundary between the body and the fluid. According to Sir George Stokes, “the force operating at the contact between a falling thing and a liquid is proportional to the velocity, the radius of the object, and the fluid viscosity.

Importance of Stoke’s Law

The significance of Stoke’s Law is as follows:

  • This law was used by Millikan to determine the electrical charge of his oil-drop experiment.
  • A person utilizing a parachute and falling from a tremendous height is protected by Stoke’s law.
  • This rule explains how a cloud forms.

Limitation of Stoke’s Law

The drawbacks of Stoke’s Law are as follows:

  • If the density difference in the equation is negative, which occurs when particles are lighter than the dispersion medium, stoke’s law is not valid. As a result, emulsion systems frequently exhibit floatation or creaming.
  • The high content of scattered solid: Stoke’s equation might not accurately represent the true sedimentation rate when the solid content of a suspension is high. On the other hand, if a proper rate of settling is to be established, the increased viscosity that high solid content provides to the system must be taken into the account. The only quantity in the equation is the medium’s viscosity.
  • Brownian movement, which is the spontaneous (zigzag) movement of particles floating in a fluid brought on by collisions with quickly moving atoms or molecules in the gas or liquid, is another factor that may have an impact on the accuracy of Stoke’s equation results. Brownian migration helps to reduce sedimentation to a certain extent. The actual rate of the sedimentation and the rate determined using Stoke’s equation differ significantly as a result.

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I am currently working with Cuemath as an online maths educator and teaching students from all over the world. Since I did my BSc in non-medical where I chose physics in my master's (MSc) and decided to deliver my knowledge to help the students in grasping the respective topics of physical sciences by having a glance at my articles.

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