1.4. Definitions and applications in fluid statics

So, as we have seen there is no relative motion between the adjacent fluid layers, therefore, the shear stress is 0 as we have already seen this in our previous lecture. So, what can be acting on the fluid surface? So, only pressure can be acting in that case on the fluid surface there is no shear only pressure forces.

In fluid statics, adjacent fluid layers do not move relative to each other. This stationary condition means that there is no shear stress generated between these layers. Since shear stress is not present, the only force acting on these layers comes from pressure. Thus, instead of having both shear and pressure forces acting, we only consider pressure forces at rest, which simplifies our analysis.

Imagine a stack of books piled on top of each other. If the books are perfectly still, they exert pressure downwards due to their weight, but there’s no sliding (shear) between the books. Similarly, in a fluid at rest, pressure acts downwards without any sliding between layers.

Gravity force acts on the fluid and that is called the body force.

In fluid statics, gravity acts on a fluid, causing it to exert pressure downwards. This gravitational effect is termed a body force since it acts on the entire volume of fluid rather than on a surface. Every part of the fluid experiences this force, contributing to the overall pressure of the fluid at varying depths.

Think of a water balloon. The weight of the water inside causes pressure at the bottom of the balloon due to gravity acting on the fluid. This pressure can lead to the balloon bursting if too much water is added, similar to how fluid pressure works in larger bodies of water.

What will be the applications of this particular thing that we are studying about pressure? We can know the pressure variation within a reservoir. So, it finds application in reservoir, we are also able to find forces on submerged surfaces you will see many cases in real life where the surfaces are submerged.

Understanding pressure and its variations is crucial in various engineering applications, particularly in reservoirs. The pressure varies with depth in a reservoir, which helps engineers determine the forces acting on dam walls and submerged surfaces. This knowledge aids in the design and maintenance of structures to withstand these forces safely.

Consider a water reservoir behind a dam. Engineers must calculate the pressure at different depths to ensure that the dam can safely hold the water. If there is too much pressure from the water above, the dam could fail, just like if a balloon is overfilled with water, it can burst.

We are also able to find using this app this principle the tensile stress on pipe walls and also we are going to see the buoyant forces because buoyancy plays an important role in this.

Buoyancy is the upward force exerted by a fluid, opposing the weight of an object submerged in it. This principle is vital in understanding how objects float or sink and is essential in engineering applications such as boats and underwater structures. By analyzing buoyancy and pressure, engineers can predict how structures will behave in fluid conditions.

Imagine a large ship floating on a lake. The buoyant force from the water is what keeps the ship afloat. If the ship carries too much weight, the buoyant force might not be sufficient, and it will sink. Engineers use calculations of buoyancy to design ships that can hold certain weights without sinking.

So, the question is, what are the pressure forces behind the Bhakra Nangal Dam? If this is the first step towards any design, you need to determine the forces or the parameters that determine the stability.

The design and construction of large structures like dams require a clear understanding of the pressure forces acting on them. For example, the Bhakra Nangal Dam must withstand significant water pressure due to the height of water in the reservoir. Engineers must calculate these forces to ensure that the dam remains stable and does not fail under pressure.

When building a sandcastle near the beach, the size and shape of the castle must be designed to withstand the waves and water pressure without collapsing. Similarly, engineers design dams to deal with the immense forces of the water behind them, preventing potential disasters.

An important question is, how do we measure atmospheric pressure. One of the simplest devices the barometers. See, what happens is that the column of liquid is held up by the pressure of the liquid in the tank.

Barometers are instruments used to measure atmospheric pressure. They work by holding a column of liquid, typically mercury, in a tube. The height of the liquid column depends on the atmospheric pressure pushing down on the liquid in the reservoir. As weather changes, the atmospheric pressure alters, causing the liquid level in the barometer to rise or fall, providing a measurement of pressure.

Think about how a straw works. When you suck on a straw, you're lowering the pressure inside the straw, causing liquid to rise up. Barometers work on a similar principle, where atmospheric pressure supports the liquid in the tube, helping us measure the pressure outside.

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