Studying Fluid Mechanics, I started to notice that almost every textbook/website uses a specific point to make calculations about the pressure in a liquid at a given depth (hydrostatic pressure): the geometric center (as shown in the images below), when presenting pressure gauges/manometers/piezometers.
Note: This happens regardless of the field to which the book is directed (I looked in textbooks of Fluid Mechanics for Civil, for Electrical, for Mechanical...).
Sources: Introduction to Fluid Mechanics - Nakayama & Boucher/Mecânica dos Fluidos - Noções e Aplicações - Sylvio R. Bistafa/Chegg
One of the textbooks I looked at even draws attention to this fact, but it doesn't explain the reason for the choice:
Note the origin of the measurement of h, in the center of the tube
Source: Mecânica dos Fluidos - Franco Brunetti
A similar behavior can be identified when textbooks present liquids in motion: they use the centerline of the pipe to make calculations/measurements. Here's an example:
Source: Fluid Mechanics for Civil Engineers - N.B. Webber
So why is the choice of geometric center/centerline of the pipe so common when measuring/calculating pressure? Some hypotheses:
- Maybe all the textbooks/websites are unconsciously copying each other?
- Maybe is this some kind of "convention"?
Note to the off-topic warning: "Questions about the physical reasoning and analysis that lead to design decisions are on topic". That's the core of my question: what is the physical reason for choosing the geometric center in fluid mechanics books. In other words, what is the physical reasoning that leads to the design decision commonly adopted by almost every textbook of choosing the geometric center/centerline of the pipe when doing pressure-related calculations/measurements.