1.8. Pressure variation with location

One of the most important question is the variation of pressure with depth in a liquid. How does the pressure vary? So, to be able to, you know, give a real feel has anyone of you have done scuba diving that you will observe that the pressure increases as then you go down. So, compared to if you are at the upper surface, than at the lower surface, at the lower depths the pressure will increase. The increasing water pressure with depth limits how deep a submarine can go. These are the 2 classical example of the variation of pressure with depth and a liquid.

This section introduces the concept of pressure variation in liquids, particularly how pressure increases with depth. As you dive into water, the weight of the water above you increases due to gravity, resulting in higher pressure at lower depths. This principle is crucial for understanding phenomena in both natural and engineered systems involving fluids.

Think of a soda can. When you shake it, the pressure builds up inside due to the liquid being agitated and the gas trying to escape. Similarly, in deep waters, the pressure builds up due to the water weight above. That's why submarines have a crush depth—beyond that, the pressure is too great for the structure to withstand, just like a soda can would burst if shaken and opened too quickly.

So, now the important question is why P increases with depth. This is a volume of liquid. As you can see there are some layers on it. So, this is one layer, right? This is one layer. So, this means, this particular layer that have to support the entire liquid that is above this layer and the same is for this layer. So, this means, this layer will have to support this much plus this much.

Pressure increases with depth due to the cumulative weight of the liquid above. Each layer of liquid exerts pressure not only from its weight but also from all the layers above it. For example, if you imagine several blocks stacked on top of each other, the block on the bottom must support the weight of all the blocks above it. This cumulative effect results in increased pressure at greater depths.

Consider walking on a pile of snow. The snow at the bottom has to support all the snow above it. The deeper you go into the snowdrift, the more pressure is exerted on the lower layers. Similarly, the further down you go in a body of water, the more water presses down on you, increasing the pressure as you go deeper.

One of the other important feature of pressure is that pressure is always perpendicular to the surface. And the pressure does depend only on depth we are going to see that will do some basic derivation later in this lecture, where you will see that the dependence of pressure is only on depth is very important to note.

Pressure acts equally in all directions and is always perpendicular to the surface it acts upon. This characteristic of pressure means that regardless of the specific orientation of that surface, the pressure exerted is the same, as long as depth remains constant. This relationship is crucial for designing structures subjected to fluid pressure.

Imagine putting a balloon at the bottom of a pool. Whether the balloon is sitting flat on the pool floor or slanted at an angle, the pressure from the water is always perpendicular to its surface, pushing in equally from all sides. This property allows engineers to predict how structures, like dam walls, will behave under pressure.

Now, some definitions and applications, in fluid statics as we have seen there is no relative motion between the adjacent fluid layers, therefore, the shear stress is 0. What will be the applications of this particular thing that we are studying about pressure?

Fluid statics, where there is no relative motion between fluid layers, leads to the understanding that only pressure forces act on submerged surfaces. This concept allows us to calculate pressure variations within reservoirs, forces on submerged surfaces, and even tensile stresses on pipe walls. Knowing how pressure behaves helps in designing safe engineering systems related to fluids.

Think of a large water tank used for irrigation. Understanding how pressure varies allows engineers to design the tank's structure so it can safely hold a certain volume of water without bursting. When you fill it, understanding the pressure at various depths ensures that the walls are thick enough to handle that pressure without any risk of failure.

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.

In the context of engineering, understanding pressure is vital for the stability and safety of structures like dams. The Bhakra Nangal Dam serves as a perfect example: the design must account for the pressure exerted by water at different levels, influencing how thick the dam's base needs to be to withstand these forces without collapsing.

Picture a stack of pancakes. If you put a heavy syrup on top of a tall stack, the pancakes at the bottom need to be thicker to support the weight above without crumbling. Similarly, the base of a dam must be thicker to support the immense pressure from the water it holds back.

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