Viscosity: Class 11 Physics Notes, Definition, Concepts, Formula, SI Unit, and Applications

Viscosity simply refers to a fluid's resistance to flow. 

Consider honey and water. When you try to pour honey into a cup, its flow is much slower than that of water, as it is thicker. Honey has more layers than water that stick to the surface of its container. The bottom layer of honey sticks to the surface while the top layer moves. 

The mechanism is such that the layers of honey at an intermolecular level are more compact than water. As they rub against each other, they experience increased internal friction. This creates viscosity. This is also the reason why you need to apply more force to a viscous fluid, such as honey, to overcome this friction and allow it to flow. You will not apply that much force when it comes to water. 

Want to brush up on what friction is? Why not practice Chapter Four’s NCERT Solutions on the Laws of Motion - it’s free to download from Shiksha!

Importance of Learning Viscosity 

• Viscosity and related concepts, such as Bernoulli’s Principle, are frequent in NEET and JEE Mains. Numerical problems related to terminal velocity, shear, and strain rate are common in these exams. 
• Mastering viscosity can be particularly helpful when aspiring to engineering branches, such as mechanical or civil engineering, as well as biomedical sciences. 

In Chapter Nine of the Class 11 NCERT Physics textbook, the definition of viscosity is 

“Most of the fluids are not ideal ones and offer some resistance to motion. This resistance to fluid motion is like an internal friction analogous to friction when a solid moves on a surface. It is called viscosity. This force exists when there is relative motion between layers of the liquid.” 

We will explain related concepts below. 

So what characterises viscosity?

It’s the intermolecular structure of the fluid that determines viscosity or the flow behaviour. But there are some other factors associated with it. 

While section 9.5 of the Mechanical Properties of Fluids introduces a few more concepts of Viscosity in passing, let’s review them quickly here. 

Laminar Flow - It’s the type of motion of some fluids where layers flow parallelly without mixing. Each layer moves smoothly over the one below it. 

$\frac{\mathrm{dv}}{\mathrm{dx}}$

dv is the small change in velocity, while dx is the small change in distance between the layers. 

Shear and Strain Rate - The interaction among fluid layers as they slide past each other creates friction. We call that shear. 

The strain rate, aka rate of shear, is the calculation of how quickly the top layer moves ahead of the bottom layer.
Numerically, when we consider laminar flow, the strain rate is equal to the velocity gradient. So we represent that as 

$\text{Strain Rate}=\frac{\mathrm{dv}}{\mathrm{dx}}$

The strain rate is another name for velocity gradient. The concepts of shear and strain rate are 

But, there is another term that may be missing when we read about the terms shear and strain rate and attempt to understand the numerical values related to viscosity more. That’s shearing stress. It’s basically the force that causes the flow of the fluid.

If you recall the previous chapter, Mechanical Properties of Solids, or have practised the NCERT Solutions for Chapter 8, you already know about it. 

But to recap here again, let’s understand shearing stress numerically. We can determine that through Force per unit area. To geek out, you can think of it like Tangential force applied, and the area over which this force is applied to. 

$\tau =\frac{F}{A}$

The usual symbol of shearing stress is τ

Let’s look into the coefficient of viscosity to understand how viscous a fluid substance is. 

The coefficient of viscosity (denoted by η, and pronounced ‘eta’) measures how much a fluid resists relative motion within its layers. 

As you read the concepts above, the internal friction within the layers depends on two factors.

• The speed at which the layers move (velocity gradient or shear rate)
• The force per unit area applied to create a flow (shearing stress)

The viscosity coefficient is the ratio of these two factors

$\eta =\frac{\text{Shearing Stress}}{\text{Strain Rate}}=\frac{\frac{F}{A}}{\frac{d}{x}}$

What is the SI Unit of Viscosity?

The Unit of Viscosity is Poiseuille or Poise, according to the NCERT book. But it is also considered the CGS (Centimetre-Gram-Second) system.  

Pascal per second (Pa·s) is the SI Unit of Viscosity and remains the most common way of expressing it. 

And, 1 Pa·s = 10 poise 

What are the Dimensions of Viscosity?

When you look at the SI Unit of Viscosity, we are measuring three things. 

• Mass of the fluid
• Length of the fluid
• Time taken for the fluid to move

So we represent the dimensions of viscosity as [ML⁻¹T⁻¹]

 

With the basics of viscosity clear, let’s move to how it directly applies. Let’s say, you want to learn the effect of viscosity.  

You must be thinking of a situation where a foreign object enters a viscous fluid. Much like putting your hand in water, it would resist it. This is a resistance or frictional force, more commonly referred to as a drag force. 

That’s what Stokes’ Law is based on. 

Stokes’ Law is a fundamental principle in fluid mechanics that mathematically describes the drag force exerted by a viscous fluid on a small, spherical object as it moves through it in laminar flow. 

The formula for Stokes Law is 

$F=6\pi \eta rv$

 η = coefficient of viscosity

r = radius of the sphere

v = velocity of the object

F = force of the object

There may be one more aspect that is essential when learning about Stokes’ Law. You learned that a viscous fluid exerts a force on an object, and also learned how to calculate this force.

Now, you may have two questions -

1. What if the object can’t accelerate and only moves at one constant speed because of the drag force?
2. Why does the object have constant speed?

Here’s what is actually happening. 

• As the object falls through the fluid, gravity is also at work. 
• But the fluid also resists this motion with the drag force and the buoyant force.
• There comes a time when the upward force balances the gravitational force. 

The net force is essentially zero. There is also no acceleration. The velocity is zero, as it stops accelerating further. That’s a constant velocity, then. That’s called terminal velocity. 

So what terminal velocity also tells us is that the drag force is velocity-dependent.