8.6.1. Measurement of Atmospheric Pressure

Now if I go for the next ones that how to get the pressure field when fluid is at the rest. That means I am just looking the what could be the functions of the P, P = P (x, y, z). If it that it is now again I am considering a very simple case, let us consider a control volume like this okay. This is what my control volume. As I said it when the fluid is at rest the shear stress become zero. So there is no shear stress component on this fluid plane. Only this normal stress which is as equivalent to the pressure will act over this control surface.

When fluid is at rest, it means there are no movements affecting its state. In this condition, the fluid does not experience shear stress – it only has normal stress, which is directly proportional to the pressure exerted on the fluid's surface. This leads us to consider how pressure varies in a control volume, described mathematically as P(x, y, z). Understanding this forms the basis for studying how pressure is distributed in different fluid contexts.

Think of a swimming pool. When there are no waves, the water is still, and the only pressure acting on the bottom of the pool is due to the weight of the water above it. Just like the still water in the pool, in a fluid at rest, pressure is evenly distributed based on the depth.

The pressure at the centre of the fluid control volume is assumed to be P (x, y, z). At that point, the gravity force is acting it which is the body force component. The gravity force what will be there? It will be unit weight multiply the volume of the control volume, which is very simple things.

Within the control volume, we not only have pressure acting but also the force of gravity, which acts as a body force. This gravitational force can be calculated by multiplying the unit weight of the fluid by the volume of that control volume. This relationship between pressure, gravity, and volume is crucial for understanding how pressure varies with depth in fluids.

Consider a soda can filled with liquid. The weight of the liquid inside exerts pressure downwards due to gravity. When you shake it, some liquid might spill, showing how the weight (gravity) of the liquid directly affects the pressure exerted at the base of the can.

All these pressure is going to act it as the Pascal law says that pressure acts normal to the surface. So that what we can consider pressures act there normal to the surface. Then we need to define now as a pressure as a x, y, z is a pressure field what we are looking it which is a function of x, y, z.

According to Pascal's Law, pressure exerted on a fluid is transmitted equally in all directions and acts perpendicular (normal) to the surface of the fluid. In practical terms, as we define pressure in a three-dimensional space (x, y, z), we can understand how pressures vary at different points based on their spatial coordinates. This forms the foundation for understanding more complex fluid behaviors.

Imagine using a syringe. When you push down on the plunger, the pressure you apply is evenly spread out throughout the fluid inside. The fluid then pushes against any surface it comes into contact with, demonstrating how pressure acts normal to surfaces.

Now the point is what we are going to discuss is that gauge pressure and vacuum pressure. Components now is coming it what is your datum to measure the pressure. Whether you have to make a absolute zero pressure, that means you have a vacuum. From there you are measuring the pressure, or you consider as local atmosphere, to measure the pressure.

When discussing pressure measurement, we must determine our reference point or 'datum.' There are two primary forms of pressure measurement: gauge pressure, which refers to the pressure relative to local atmospheric pressure, and absolute pressure, which measures pressure relative to a perfect vacuum. This distinction is crucial for accurately understanding pressure in different contexts.

Think of a car tire. The gauge pressure is what the tire pressure gauge reads compared to current atmospheric pressure; if it says 30 psi, it's 30 psi above the atmospheric pressure. Absolute pressure, on the other hand, would be 30 psi plus the weight of the atmosphere on top of it. This means the car tire may be under a much higher actual pressure than we feel.

So when you measure the atmospheric pressure is a datum. There is a two conditions is comes it. One will be the pressure above the atmospheric pressure, another one will be the pressure below the atmospheric pressure.

To measure atmospheric pressure, we use barometers, which can indicate the pressure above or below atmospheric levels. A common type is the mercury barometer, where the height of the mercury column can infer atmospheric pressure. Understanding these measures helps to predict weather changes and comprehend buoyancy and fluid dynamics better.

Imagine an old-fashioned mercury barometer like the ones used many years ago. The glass tube filled with mercury would rise or fall based on the atmospheric pressure—much like how a tide rises and falls with the moon's gravitational pull. Just as you can predict high or low tides, atmospheric pressure can help forecast weather conditions.

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