1.3. Indian Institute of Technology - Kharagpur

So, this is the week 10, lecture number 1, here we are going to study about the topic that is mentioned in this slide, this is about viscous fluid flow. Actually, you have, we have gone through this topic before but in a much more crude manner. The main objective of this module is going to be able to derive Navier Stokes equation from scratch, so how to start from the beginning and derive the Navier Stokes equation.

In this section, we are introduced to the topic of viscous fluid flow. The instructor emphasizes that while students have been exposed to this topic before, the current focus will be on a deeper understanding of the fundamentals, specifically through deriving the Navier-Stokes equation. This equation is crucial in fluid dynamics as it describes how fluids move. The instructor aims to break down the process step-by-step.

Think of learning to ride a bicycle. At first, you may only manage to balance and pedal without understanding how everything works together. As you practice, you start to understand how the gears operate, how the brakes function, and how to steer effectively. Similarly, the lecture aims to deepen your understanding of fluid flow, moving from basic concepts to more complex equations.

A fluid is a substance that deforms continuously under the action of a shear force, this means, it cannot resist shear. A solid however, can resist shear and remain at rest.

Here, we learn that fluids are materials that cannot maintain shape when force is applied. For instance, when water (a fluid) is poured, it takes the shape of its container, while a solid, like a block of wood, will maintain its shape unless a significant force is applied. This difference is fundamental in understanding fluid mechanics.

Imagine spreading peanut butter on bread. The peanut butter (fluid) spreads easily and conforms to the surface of the bread. In contrast, a piece of hard cheese (solid) would stay in its shape unless you applied enough force to cut through it. This analogy helps to illustrate how fluids behave under different conditions.

In fluid mechanics, a matter is classified into fluids and non-fluids. So, in thermodynamics, the normal definition is classification in solids, liquids, and gases. But in fluid mechanics, it is fluids which consists of gases and liquids and non-fluids; non-fluids are mostly the solids.

This section clarifies how matter is categorized in fluid mechanics. Unlike thermodynamics, which includes solids, liquids, and gases, fluid mechanics focuses mainly on fluids—both liquids and gases. Non-fluids, which generally means solids, do not flow and are therefore treated differently in the study of fluid dynamics.

Think of a river. The water (liquid) flows freely and can take the shape of its container (the riverbed). Now picture a rock on the riverbank; it remains in place and holds its shape. In fluid mechanics, we pay attention to the flowing nature of water as a fluid and treat the rock as a non-fluid solid.

Another basic revision is properties of fluid, so first is kinematic property, that is, velocity, acceleration, vorticity, rate of strain, angular velocity etc. So, there are many other properties like this kinematic.

This part introduces us to the key properties of fluids, starting with kinematic properties. These include parameters that describe the motion of fluid particles, such as their velocity and acceleration. Understanding these properties is crucial for analyzing how fluid behaves under different conditions.

Consider driving a car on a smooth road. The speed of the car is similar to the velocity of fluid; how quickly you accelerate is akin to changes in the fluid's acceleration. Just like understanding your car's controls helps you drive, grasping fluid properties helps engineers design systems that manage fluid flows efficiently.

Transport properties, you know, are viscosity, thermal conductivity, mass diffusivity. Thermodynamic properties like density, pressure, temperature, entropy, enthalpy etc.

Transport properties are characteristics that describe how fluids interact with their environment, such as viscosity (how 'thick' a fluid is), thermal conductivity (how well a fluid conducts heat), and mass diffusivity (how substances spread through a fluid). Thermodynamic properties, like density (mass per volume) and pressure (force exerted by the fluid), influence how fluids behave in various situations, which is critical for engineers.

When you pour syrup onto pancakes, its viscosity slows down the pouring, making it thick compared to water, which flows easily. This is similar to the way different fluids behave based on their transport properties. Understanding these properties helps engineers predict how fluids will behave in pipes, pumps, or any processing systems.

So now we go into little bit more detail in kinematic properties. So, the idea of this particular lecture today is that we are going to write what actually material derivatives are and we see the rotation you know how the fluid particle gets rotated and try to obtain the strain rates and those quantities...

The focus now shifts to a deeper exploration of kinematic properties, particularly the concept of material derivatives, which describe changes in a fluid property as it moves with the flow. Understanding how fluid particles rotate and deform is vital for analyzing their behavior and deriving equations that govern fluid motion.

Imagine watching leaves floating down a stream. They not only move forward (which relates to velocity) but also spin and drift on the water's surface. Just like the leaves, fluid particles rotate and change as they move through different conditions in a fluid flow, which is what we will explore here.

--