Area unit for mmHg pressure

Question

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?

Answer 1

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}

Answer 2

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.

Answer 3

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.

Answer 4

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.

Answer 5

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..