1.1.1. Lecture - 13

Welcome all of you to Fluid Mechanics course. Today we are going to solve the problems on fluid statics. Looking that today I will cover with an introductions to hydrostatic bench experiment.

This introduction sets the stage for learning about fluid statics, specifically focusing on practical applications. The hydrostatic bench experiment is highlighted as a pivotal experiment that helps visualize and understand how fluids behave at rest. It introduces key concepts and sets goals for the lecture.

Think of fluid statics like a still pond. When you throw a stone into the water, the ripples you see are changes in fluid motion, but before the stone is thrown, the water is at rest—much like how we focus on static scenarios in fluid mechanics.

Now let us look at the hydrostatic bench experiment setup, which is there in IIT Guwahati. So this type of experimental setups which is called this hydrostatic bench experiment setup, you can see the pressure gauge, you can see the pressure gauge. You can see this mercury manometers. So these mercury manometers are there.

In this chunk, the equipment used in the hydrostatic bench experiment is presented. Instruments like pressure gauges and mercury manometers are crucial for measuring fluid pressure accurately. Understanding how to use these tools is essential for conducting experiments in fluid mechanics.

Imagine measuring blood pressure at a doctor's office. A sphygmomanometer, much like a pressure gauge, indicates how much pressure applies to the blood vessels. Similarly, in fluid mechanics, we measure the pressure within fluids using specialized tools.

And you can have conduct different experiments using this pressure gauge as measurements, the manometer measurement, and U-tube manometers.

This section discusses the various methods of measuring fluid pressure using different types of manometers. Each device provides insight into fluid behavior under static conditions, which is essential to accurately understanding fluid mechanics.

Consider how a thermometer measures temperature for us. Just as a thermometer provides vital insight into temperature changes, manometers give insights about pressure in fluids—both are fundamental in their respective fields.

Not only that, there is the experiment setups to prove the Pascal's laws that the pressure in a horizontal surface remains consistent.

This chunk introduces Pascal's principle, which states that fluid pressure transmitted in a contained fluid is equal in all directions. Understanding this principle is critical when analyzing how fluids distribute pressure and how it influences structural designs.

Think of a syringe. When you push down the plunger, the pressure you apply is distributed evenly throughout the fluid, demonstrating Pascal’s law. This is similar to how fluid pressure works in any closed system.

Now let us i just write the formulaes, okay. And just to repeat the things what we learnt it in fluid basic properties and the fluid statics that the Newton's laws of viscosities we established the relationship between shear stress and the velocity gradient.

In this section, the lecture begins to cover the fundamental formulas necessary for fluid static problems, including Newton's laws regarding viscosity. Understanding these formulas is crucial for solving practical problems in fluid mechanics, particularly those pertaining to fluid flow and behavior.

Imagine stirring honey with a spoon—the viscosity of honey affects how smoothly you can stir. The formulas regarding shear stress relate closely to how different fluids behave under force, similar to the way honey flows differently than water.

As you know very basic things, when you consider z as a at the free surface level is zero. As z increases in the downwards the pressure will be P = ρgh.

This part explains the concept of pressure distribution in a fluid at rest. The formula P = ρgh shows how pressure increases with depth due to the weight of the fluid above. This principle is foundational for understanding hydrostatics and predicting fluid behavior under static conditions.

Picture diving into a swimming pool. As you swim deeper, you feel more pressure on your ears—the pressure increases with depth, just as the formula describes. This real-world experience connects students to the theoretical concepts of fluid pressure.

Let us start to solve the problems, these very easy problems that there is a square gate of a dimensions of 1.5 meter into 1.5 meters.

This section transitions into applied examples, indicating the hands-on approach of using theoretical principles to solve specific fluid static problems. By working through problems step by step, students apply what they have learned while reinforcing their understanding.

Imagine you're a builder checking how much water pressure a dam will exert on a gate. Solving problems like this enables engineers to ensure the safety and effectiveness of their structures, making fluid mechanics both exciting and practical.

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