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Many textbooks mention that the height of a column of mercury in a mercurial barometer is 29.92" Hg under standard atmospheric conditions.

However, they usually do not mention the diameter of that column, or whether the size of that diameter matters at all.

Let's consider a narrow column of arbitrary height and a wide column, relatively speaking. Since it is narrower, there is less volume of mercury per inch of that tube, so it seems that the narrow column would have to be higher than that of the wide column to balance the mercury in the reservoir that rises from the surrounding pressure.

Should I conclude that those who designed mercurial barometers used a specific diameter (which sounds unlikely and impractical?), or is there something I am not considering here that makes the diameter of a mercurial barometer not relevant to the height of the column, under standard conditions?

By the way, I have a hunch the surface area of the reservoir surrounding the column doesn't matter for some clever reason, but it still seems to me that the diameter of the column does. Would love it if this were true of the diameter as well.

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The reading furnished by a mercury manometer does not depend on the cross-section of the tube with the mercury in it, so long as it is large enough to not suffer from capillary effects. Manometer manufacturers know this, and size the inside diameter of the tube accordingly.

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  • $\begingroup$ Thanks for your response! Wondering how the height does not depend on the diameter? $\endgroup$
    – septimyr
    Commented Apr 14, 2022 at 21:13
  • $\begingroup$ Imagine two identical manometer tubes, measuring the same pressure and having the same amount of mercury in each. Now imagine joining the tubes together at the bottom of the "U" shape on each. what will happen? $\endgroup$
    – niels nielsen
    Commented Apr 15, 2022 at 2:49

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