7.1.1. Lecture - 04

Welcome all of you for this lecture on fluid mechanics. Today we will discuss about fluid statics that means fluid at rest.

In this introduction, the professor welcomes students to the lecture on fluid mechanics, specifically focusing on hydrostatics, which is the study of fluids at rest. It emphasizes that understanding fluids when they are not in motion is essential for analyzing various fluid behaviors and characteristics.

Think of a still pond where the surface is calm. The behavior of the water in the pond is an example of hydrostatics. Understanding how the water pressure at different depths affects the pond's edges is crucial in fields like civil engineering.

Before starting this lecture, again I want to repeat the reference books, like the most illustrations books like the Cengel Cimbala book which is very good book in terms of lot of illustrations, the examples, and the exercise what is given in Cengel Cimbala book.

This chunk emphasizes the importance of reference materials that aid in understanding fluid mechanics. It mentions three specific books—Cengel Cimbala, F.M. White, and Bidya Sagar Pani—each useful for different learning styles, from detailed illustrations to concise problem-solving techniques.

Consider a student learning to cook. Some may follow a recipe book with step-by-step pictures (Cengel Cimbala), while others might prefer a concise cookbook that requires prior knowledge (F.M. White). Both types of books can help in becoming a better cook, just as well-chosen reference books help in mastering fluid mechanics.

Now let us come to the contents of the today lectures. The first I will discuss what we so far in the last three lectures we discussed it.

Here, the professor outlines the structure of the current lecture. The lecture will recap previous content and then segue into new concepts, namely hydrostatics, Pascal's law, pressure forces on fluid elements, and various types of pressure, including gauge and vapor pressures.

Imagine an artist preparing for a new painting. They first review their previous artworks to gather inspiration before starting the current piece. In the same way, the lecture builds on previous concepts to prepare for new learned material.

Now let us come to the very basic concept what we are talking about the fluid at rest. So the basically we are talking about now, the fluid at rest, okay? If it is a fluid is at rest, it is a very simplified problem now.

This chunk introduces the definition of fluid at rest. When fluid does not move, its velocity becomes zero. The pressure field becomes the primary focus since there are no velocity gradients, and by Newton's laws, this results in no shear stress, simplifying the problems to primarily understanding the pressure distribution within the fluid.

Think of a cup of coffee sitting on a table. The coffee is fluid at rest, meaning there’s no swirling or movement. The pressure at the bottom of the cup is due to the weight of the liquid above it, and this is what needs to be considered when assessing how the cup supports the liquid.

And what the two forces we have? The gravity force and the force due to the pressure distribution.

In this section, the discussion focuses on the forces acting on fluids at rest. There are two main forces: gravitational force, which pulls the fluid down, and the pressure force arising from the weight of the fluid above it. In equilibrium, these forces must balance to maintain the fluid at rest.

Consider a large balloon filled with water. The force of gravity pulls down on the water, while the pressure from the water inside pushes against the walls of the balloon. If the water were to start moving, the forces would change, but as it sits still, these forces are balanced.

So we need to know it what is the fluid pressure is going to act on this dam, on these vertical surface and also the inclined surface.

The importance of understanding hydrostatic pressure distribution is emphasized, particularly in practical applications like dam design. Hydrostatic pressure acts perpendicularly to surfaces, and different surface orientations (like vertical or inclined) will experience different pressure distributions.

Imagine the pressure exerted by water on a submarine at various depths. The deeper the submarine dives, the greater the water pressure becomes due to the weight of the water above, affecting the submarine's structural integrity.

Now let come it to very basic law is called Pascal. As you when you fluid is rest let us consider is that the there will be a normal stress acting on any plane.

Pascal's Law states that in a fluid at rest, pressure is exerted equally in all directions. This means if you increase pressure at one point in a confined fluid, it will be felt equally throughout the fluid. The law helps understand how pressure is transmitted in fluid systems, like hydraulic systems.

Consider a balloon filled with air. If you squeeze one part of the balloon, that pressure is felt throughout the entire balloon's surface. Just like the air in the balloon, when a fluid is at rest, any applied pressure affects the entire fluid uniformly.

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