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Atmospheric pressure is stated as 14.7 pounds per square inch (square inch is the area unit). When mmHg is utilized, what is the area unit? For example, if blood pressure is "120", does that mean 120 mmHg per square millimeter?

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    Also relevant to consider that we almost always (and especially in medicine) talk about gauge pressures/pressure differences. When we say blood pressure is "120 mmHg" in absolute terms we mean "120 mmHg above the atmospheric pressure".
    – Bryan Krause
    Mar 27 at 16:03

5 Answers 5

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My physics is a bit rusty, but the equation for pressure of a liquid is

p = ρgh

where rho is the density, g is the local gravity and h is the height of the column of liquid. As you can see from this equation, the pressure of liquids is independent of the area underneath it.

So whether you built a mercury manometer with cylindic base of 1cm2 filled with Hg or a cylindic base of 1dm2, the amount of height that the liquid rises due to increased pressure stays the same.

Wikipedia states that

[b]ecause pressure is commonly measured by its ability to displace a column of liquid in a manometer, pressures are often expressed as a depth of a particular fluid

The pressure exerted by a column of liquid of height h and density ρ is given by the hydrostatic pressure equation p = ρgh, where g is the gravitational acceleration. Fluid density and local gravity can vary from one reading to another depending on local factors, so the height of a fluid column does not define pressure precisely.

https://en.wikipedia.org/wiki/Pressure#Units

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    1mm^2 cross section won't work well because of capillary action. 1cm^2 should be ok.
    – DavePhD
    Mar 28 at 22:49
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As per Narusan's answer, it's an artifact of the method of measurement from using a column of mercury in a curved vacuum tube.

Equivalent of 7.50062 mm of mercury is 1 kPa, or 0.150 psi or 10 millibars.

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When looked at dimensionally, "mmHg" as a pressure measurement is "cubic millimeters of mercury per square millimeter". Basic dimensional analysis says that you can cancel your volume with your area, leaving only a length.

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Consider a liquid of density ρ and volume V, its weight on the ground is:

p = ρ V

If this volume of liquid is a column of constant cross-section s over a height h, then:

p = ρ h s

The pressure this liquid exerts on its base surface, which is s, is:

P = p / s = ρ h s / s = ρ h

So, in the end, this pressure depends only on the height of this liquid column.

Then there is no surface dependance to evaluate a pressure as a height of any liquid.

For example, one atmosphere is at the sea level:

10 m H₂O
76 cm Hg

Mercury was used here because it's more practical to manipulate than a 10 m column of water.

In the practical case where your blood pressure is evaluated to 120 mm Hg, This means your blood pressure is 12 cm Hg above 1 atm.

( 76 + 12 ) cm Hg = 88 cm Hg

This is a pressure of

( 88 / 76 ) atm = 1.15 atm

or 15 % above the atmospheric pressure at sea level. This is also the pressure of 1.5 m of water, the pressure you feel when you swim 1.5 m below the water surface.

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Please note that my initial question compares psi to mmHg as if they’re similar things; that was my incorrect understanding. I had been viewing “mmHg” as “pressure”. Millions of people today are being told their blood pressure is a number with “mmHg”. But mmHg is a statement of distance; there is no force or area. It is not utilized in pressure calculations. I came to realize this the day after I posted the question.

I could now revise my initial question to, “When the nurse says our BP is 120/80, what is the actual pressure (force over area) on the aorta walls when the left ventricle contracts to push a small volume of blood (systole)”?

The relationship of mmHg to psi in atmospheric pressure helps to answer that. One Earth atmosphere at sea level is 14.7 pounds per square inch. (Not sure how they determine that, but it’s accepted.) That pressure on a barometer pushes mercury to a height of 76 cm or 7600 mm. There are two interesting numbers from that relationship: 517 mmHg for each psi and 0.00193 psi for each mmHg. (7600 / 14.7 = 517. 14.7 / 7600 = 0.00193) I suggest these are valuable factors for Dimensional Analysis.

Sorry: numbers are wrong but concept remains. Edit: 7600 mm should be 760 mm. (10 mm in each cm) Edit: 7600/14.7 should be 760/14.7=51.7. Edit: 14.7/760=0.019. Edit: Two numbers: 51.7mmHg for each mmHg, 0.019psi for each mmHg.
Edit: Correction on planet: On another planet, if a barometer shows 120 mmHg, the atmospheric pressure is 2.28 psi (120 x 0.019) same as BP 120.

To answer my initial question, the pressure statement is independent of the mmHg factor. When talking about planetary pressure, “pounds/square inch” is OK. When talking about blood pressure, “grams/square mm” may be preferred.

Note that a blood pressure monitor starts with the actual physical pressure and changes it to a number (a distance value) we can easily remember. Could the monitor be reverse-engineered to find the actual pressure? Finding the pressure at the aorta (or left arm) is important when considering the pressure in other parts of the circulation system, at capillary beds etc..

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    Eh, this is wrong. "mmHg" is pressure as much as anything else is pressure. Specifically, it's defined as the force exerted by 1 millimeter of mercury at standard gravity and 0 degrees C. That's as much a unit of pressure as a "pound" (lbf) is, which is the pressure exerted by a mass of one pound at standard gravity. When you're specifying a particular mass you have to also specify the area at which that mass is divided whereas a height of mercury is taken at some point, there's no actual difference when you look at the dimensionality.
    – Bryan Krause
    Mar 28 at 17:05
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    GenAIs are not intelligent. They just regurgitate text that's similar to their training data. Needing to specify the area when expressing "PSI" is not because you need a "per area" to express pressure, but because "pound force" is not a pressure. The SI unit of pressure is a Pascal, you don't need Pascals Per Area, just Pascals. You don't get a different number of Pascals when you apply the same pressure to a larger area, it's still a Pascal. You don't get a different number of mmHg when you apply pressure to a larger area, it's still a mmHg of pressure.
    – Bryan Krause
    Mar 28 at 19:46
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    See also Narusan's answer for the concept and Jiminy's for the conversions. mmHg can absolutely be used in calculations.
    – Bryan Krause
    Mar 28 at 19:51
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    It’s a bit like using a light year to measure distance. No one is pretending that there’s a time unit in the dimensions of a distance. It’s just a way of expressing a distance that is exactly equivalent to 9.461 × 10^15 metres. Similarly 1 mmHg = 133.322 Pascal.
    – Chris
    Mar 28 at 22:12
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    Also, I see where you’re going with “grams/square mm is preferred”, but if you’re paying attention to dimensionality, it’s force per unit area, and the gram is a unit of mass, not force. This is true for pounds as well of course! That’s why saying things like mass per unit area depends on the gravity where you are.
    – Chris
    Mar 28 at 22:25

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