1.1. Prof. Mohammad Saud Afzal

Welcome students. 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 introductory segment, the professor welcomes the students to the first lecture of week 10, focusing on viscous fluid flow. He acknowledges that they have previously encountered this topic but in a less detailed way. The main aim of the module is to derive the Navier-Stokes equation, which is fundamental in fluid mechanics, from the ground up, ensuring that students grasp the entire derivation process.

Think of the derivation of the Navier-Stokes equation like building a house. In a previous course, the students might have seen a house in its initial stages, like just the foundation without walls or a roof. Now, in this module, they will learn how to construct each section of the house step by step, ensuring everything is well-built and understood before they move to the next parts.

And we are expecting to dedicate around depends but at least 3 to 4 lectures in this module and our difference from the regular classes to this one is going to be that I will be teaching it by hand, we will take the help of slides as little as possible, because Navier Stokes equation is something that needs to be done by hand and in the derivation using the slide, it has been found out it is not helpful that much for this particular thing.

The professor anticipates that this module will take about 3 to 4 lectures. He emphasizes that the teaching approach will differ from regular classes, as he plans to perform derivations manually on the board rather than relying on slides. This hands-on approach is deemed necessary for comprehending the complexities involved in the Navier-Stokes equation.

Imagine learning to ride a bicycle. You can watch videos or read about it, but until you actually sit on the bike and balance yourself, practicing is the best way to learn. Similarly, the professor believes that writing down the equations by hand will help students learn more effectively than just looking at slides.

So, to start with this one, some general, you know points; one is 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.

The professor explains that a fluid is defined as a material that continuously deforms when subjected to shearing forces, indicating that it cannot maintain its shape when force is applied. In contrast, a solid maintains its shape and resists such forces.

Consider how honey behaves compared to a block of wood. When you pour honey, it flows and changes shape easily because it cannot resist shear forces. On the other hand, the wood block stays intact whether you push it or not. This difference illustrates why fluids and solids have distinct behaviors under stress.

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.

The classification of matter in fluid mechanics is based on its ability to flow. Fluids encompass both gases and liquids, while non-fluids are primarily solids. This distinction highlights the different behaviors that materials exhibit when subjected to forces.

Think about pouring water (a fluid) from a glass compared to trying to pour a piece of rock (a solid). The water flows freely and takes the shape of whatever container you put it in, demonstrating fluid behavior, whereas the rock stays the same shape and does not flow.

So, another basic revision is properties of fluid, so first is kinematic property, that is, velocity, acceleration, vorticity, rate of strain, angular velocity etc.

The professor reviews fluid properties, starting with kinematic properties, which include velocity, acceleration, vorticity, rate of strain, and angular velocity. These properties describe how fluids behave and change when in motion.

Consider how water flows down a river. The velocity tells us how fast it's moving, the acceleration indicates how quickly it speeds up or slows down, and vorticity describes the swirling motions you might see. These terms help us understand the dynamic nature of fluid movement.

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