18.1.3. Indian Institute of Technology Guwahati

Welcome all of you to fluid mechanics course. Today, I am going to deliver lecture on conservation of momentum. As you know, in the last class we discussed about conservation of mass. Also, we have solved few problems based on the conservation of mass.

In this introduction, the speaker welcomes students to a course on fluid mechanics, specifically focusing on the principle of conservation of momentum. This follows a previous lesson on conservation of mass, illustrating a structured learning approach where concepts build upon one another. The mention of having solved problems indicates an interactive and practical approach to learning fluid dynamics, where students apply theoretical knowledge.

Think of this course like building a house. First, you need a solid foundation (which represents the conservation of mass), and then you can start framing the walls (the conservation of momentum) to create a robust structure. Each part is crucial to the overall integrity of the house.

Basically, we have been following the Reynolds transport theorem as a basic concept to apply the setup of the system into physical equations to the control volume level.

The Reynolds transport theorem is a fundamental principle in fluid mechanics that relates the rate of change of a system to the transport of fluid through a control volume. It serves as a bridge between differential and integral forms of equations, enabling the application of conservation laws to fluid motion. Specifically, in this context, it helps in deriving equations governing mass, momentum, and energy in the fluid flow.

Imagine a river flowing past a fixed point. The Reynolds transport theorem allows us to understand how water moves into and out of a specific area (the control volume) and how that affects everything around it. Just like measuring the amount of rainwater that enters and exits a bucket over time, we can analyze the flow of fluid through any designated space.

We have two basic assumptions, that is, with respect to time is it a steady or unsteady. So, the steady we do the approximations of many fluid flow problems which are steady problems.

In fluid mechanics, one of the key assumptions we make is whether the flow is 'steady' or 'unsteady'. A steady flow means that the fluid properties at any given point do not change over time, while unsteady flow indicates that they do. This distinction is crucial as it simplifies the analysis. By classifying problems based on these assumptions, engineers and scientists can apply appropriate mathematical models to predict fluid behavior.

Think about standing in a flowing river. If the water level and speed remain constant while you stand there (steady), you can predict how the water flows around your legs. However, if the water rises unexpectedly (unsteady), you must continuously adjust your position. Similarly, understanding whether a fluid flow is steady helps engineers predict behavior accurately.

When you have a steady incompressible flow, most of the cases what we consider for flow devices or engineering applications, we can consider steady incompressible flow.

In many engineering applications, particularly in fluid mechanics, flows are often assumed to be both steady and incompressible, meaning their density does not change as the fluid moves. This assumption simplifies calculations considerably, allowing engineers to focus on velocity and pressure without worrying about changes in fluid density that can complicate the analysis. As a result, formulas for mass and momentum conservation can be applied more easily.

Think of a garden hose with water flowing steadily out. If you keep the water pressure the same (steady), the flow rate remains constant, and you can easily predict how long it will take to fill a bucket. If the pressure fluctuates or the hose is kinked, the flow will be inconsistent and unpredictable, similar to unsteady flow in fluid mechanics.

If you look at this project which was initiated or commissioned early in 1950s and 60s, generating and installing hydro power projects about 1300 megawatt power.

This part highlights real-world applications of the principles discussed. The Bhakra Nangal project is cited as an example where understanding fluid mechanics is crucial in designing large structures like dams. These projects rely on principles of fluid dynamics to estimate power generation capacity and manage water flow effectively, indicating the relevance of theoretical concepts in practical scenarios.

Imagine building a dam to hold back a river; if you understand how much water flows and how it behaves (fluid mechanics), you can design a structure that holds strong against its force. Just like architects must consider wind and rain in building designs, engineers use fluid mechanics to ensure that their dams can handle the natural flow of water efficiently.

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