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...). Images sources: MATHalino/PennState College of Engineering (MNE)/The SensorsGuide/University of Sydney (MDP)/ScienceStruck/Chegg
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"?
- Maybe it is because a point in the horizontal plane of the geometric center gives the average pressure of a tank?