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Studying the basic concepts of Fluid Mechanics, applied to pressure gauges, and looking at schematics in many places, a question came into my mind: Where is the right place to put the pressure gauge to measure the pressure of a tank?

                          

The first case would be if the tank contains a gas. In this situation, Çengel's Fluid Mechanics book clarified it to me:

Since the gravitational effects of gases are negligible, the pressure anywhere in the tank and at position 1 has the same value.
                                            

Thus, I can put it anywhere in the tank if it contains a gas.

The second case would be if the tank contains a liquid, especially when the tank is large. In this situation, the decision that seems more logical to me is to put the pressure gauge in the bottom of the tank. However, in all the places that I looked, the point "A" was the chosen one to measure pressure (as shown in the images below in points M, N, A and B), which I believe that gives the average pressure of the tank because the point is located at height of its geometric center: $$p_{average}=\frac1H \cdot\int_0^H\gamma h \,dh=\frac{\gamma H}{2}=p_A$$ enter image description here     Images sources: MATHalino/PennState College of Engineering (MNE)/The SensorsGuide/University of Sydney (MDP)/ScienceStruck/Chegg

So, where is the right place to put it to measure pressure of a tank? Why the points M/N/A/B were chosen instead of the botton of their tanks to calculate the pressure in the images above?

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The location depends on why you are measuring the pressure. There will be a process reason for the pressure measurement, and that will determine the location of the pressure measuring device. Ex: it's possible to infer tank level from pressure. In that case, you probably want the pressure measurement at the bottom of the tank. On the other hand, if you are worried about something in the vapor space of the tank, you want the pressure measurement on the top of the tank.

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    $\begingroup$ +1 From an egineer perspective you will put it where the maintenance guys can get easy access to it $\endgroup$
    – jean
    Oct 24, 2018 at 16:02
  • $\begingroup$ @jean, agreed. But there are options. For a "bubbler" level transmitter, the pressure needed to force a small nitrogen flow to the bottom of a vertical tube is proportional to the depth of the liquid that the tube is immersed in. This means that you can position a dp cell at the top of the tank and the end of the tube at the bottom of the tank. Or, you could put a pressure tap at the bottom of the tank and mount a dp cell outside the tank at the bottom. In any event, I agree that maintenance people need access to the equipment. $\endgroup$
    – David White
    Oct 24, 2018 at 17:33
  • $\begingroup$ @DavidWhite So why most textbooks and other sources, regardless of the field (I looked in textbooks of Fluid Mechanics for Civil, for Electrical, for Mechanical...) when presenting manometers/pressure gauges/piezometers at introductory level, use the point "A" (geometric center)? Maybe "all of the textbooks are unconsciously copying each other" as DisplayName said in the comments? $\endgroup$
    – Vinicius ACP
    Oct 24, 2018 at 19:15
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    $\begingroup$ @ViniciusACP, I think you may be reading too much into the textbook pictures. Those pictures represent a very general view of the process. The particular application determines the details. How do I know? I spent 15 years doing process control for a major petrochemical company, and several of those years involved instrumentation. $\endgroup$
    – David White
    Oct 24, 2018 at 19:23
  • $\begingroup$ @DavidWhite, Sorry, I think I didn't express myself well. I was not doubting your answer. I simply don't understand why they 99% of the time choose the geometric center, regardless of the field to which the book is directed, if, as you said, "There will be a process reason for the pressure measurement, and that will determine the location of the pressure measuring device.", and the process reasons vary from field to field. "You may be reading too much into the textbook pictures", I think you're right. $\endgroup$
    – Vinicius ACP
    Oct 24, 2018 at 19:40
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In general, there is no "pressure" to measure, because pressure is a field with one pressure at each place. You can measure the pressure anywhere you like, and that will be a correct measurement of the pressure at that location. Often there is only one system variable (head if the tank is open to the atmosphere, system pressure if it is compressed), which means that given one pressure measurement the pressure anywhere else can be solved for. Of course there are some engineering motivations for choosing some spots over others.

If you don't put it at the bottom, your gauge will quit working whenever the tank level drops below wherever you mounted it. In real engineering situations, when the bottom of the tank has a complicated shape (due to submerged equipment for example) it can simplify things to put the gauge above the "complicated" volume so that the fluid above the gauge always has a simple shape.

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  • $\begingroup$ +1 But I think you might clarify the first sentence to say that in general there is not just one single pressure; the pressure varies from point to point. This is implied by calling it a "field" but that usage might be unfamiliar to someone asking this kind of question. $\endgroup$
    – Mike
    Oct 24, 2018 at 0:21
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    $\begingroup$ That's a good point. I edited the comment. $\endgroup$
    – Display Name
    Oct 24, 2018 at 0:37
  • $\begingroup$ @DisplayName So, the fact that all textbooks/websites choose "A" instead of "B" when treating pressure gauges/manometers/piezometers is actually some sort of "convention" that everyone follows? $\endgroup$
    – Vinicius ACP
    Oct 24, 2018 at 15:53
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    $\begingroup$ @ViniciusACP In civil engineering it is typical to put the sensor at the bottom, because you're usually measuring tank level. If every textbook in your field does it a certain way then it might be best to find an engineer in that field and ask them - at the end of the day it is an engineering choice. (However, for what it's worth the idea that all of the textbooks are unconsciously copying each other is a very plausible one. I see that appear to happen a lot.) $\endgroup$
    – Display Name
    Oct 24, 2018 at 16:12
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    $\begingroup$ At the very least, every point horizontally co-planar with point A (in the center) would produce the same pressure reading. As a result we can conclude there is at least some kind of convention-following going on. $\endgroup$
    – Display Name
    Oct 24, 2018 at 22:05
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Unlike a sensor, a gauge has to be where you can see it. Often you dont want the process liquid to get in the gauge, so the gauge is on top of the liquid level.

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    $\begingroup$ Other practical concerns: access for maintenance, plugging with tank bottoms, relative difficulty installing the gauge, etc. $\endgroup$
    – elliot svensson
    Oct 24, 2018 at 14:02
  • $\begingroup$ ...number of breaches of the pressure vessel... $\endgroup$
    – DevSolar
    Oct 24, 2018 at 15:15
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You are trying to find a practical solution for a theoretical problem. In order for that to work, you have to first turn your theoretical problem into a practical problem. There is so much information to be derived from a tank with the help of a pressure gauge, that there is no one 'right' solution, unless you get specific.You can basically measure whatever it is, that makes the gauge needle move, at any point it does so discretely.

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The place where the pressure is maximum. It depends upon the upper height in the most of the cases because if height increases the pressure decreases.

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