Stokes Law Derivation: Overview, Questions, Preparation

Stokes law can be defined as the force applied on a material or a body when it is left off in the liquid. At first, the velocity will remain low because of the low viscous force applied to it. But as it comes near the ground’s surface, the acceleration will increase, and the body will gain weight and the velocity of the weight increases with it.  When the body comes in contact with the liquid, the velocity of both and liquid will become constant. Any movement that happens in the liquid or fluid of the object will cause motion, and it will develop an active force that will increase the velocity of the body.

Stokes law was named after physicist George Stokes, he discovered the formula in 1851 which is as follows:

Here, F is the frictional force,

N is the viscosity,

R is the radius,

And, V is the velocity.

The force that acts on the sphere in Stokes law is called viscous force. It is directly proportional to:

• Radius
• Coefficient
• velocity

the equation is represented as:

F ∝ ηa rb vc 

By evaluating the values of a, b, c, we get:

F = k ηa rb vc (1)

The dimensions of the parameters are written below,

[MLT–2] = [ML–1T–1] a [L]b [LT-1]c

By simplifying the above equation, we get.

[MLT–2] = Ma ⋅ L– a + b + c ⋅ T–a–c (2)

Let us equate the mass, length, and time in the equation, we will get

a = 1 (3)

–a + b + c = 1 (4)

–a –c = 2 or a + c = 2 (5) 

By 3 and 4, we get

1 + c = 2

c = 1 (6) 

put the values of (3) & (6) in (4), we get

–1 + b + 1 = 1

b = 1 (7) 

Putting the value of (3), (6), and (7) in (1), we get the equation:

                          F = kηrv

In the current year 2021, the chapter of fluids’ properties holds a significant weightage of 6 marks in total. It consists of one objective type question (1 mark), one very short question ( 2 marks), and one short answer type question (3 marks). Stokes law derivation is essential and could be asked as a short question in the exam.

• Example with an equational example the proportionality and factor dependency of viscous force.

The force that acts on the sphere in Stokes law is called viscous force. It is directly proportional to - Radius, Coefficient, and Velocity. The equation is represented as: 

F ∝ ηa rb vc

• Write the final derivative output of the Stokes law. 

                          F=kηrv

• Let’s consider an example in which a drop of water is falling from the air with a coefficient value of η, and it has attained a constant velocity of v. What would be the resultant force on this drop?

If the drop has a constant velocity, the force applied would be zero. 

Q: Who discovered Stokes law and when?

Q: What do you understand by Stokes law?

Q: What is the formula used for Stokes law?

Q: What does ‘N’ represent in Stokes law?

Q: What do you understand by viscous force?