The **absolute pressure** it is the one that is measured in comparison with the absolute vacuum, for which it is always a positive quantity. This makes sense, since in a vacuum there is no matter that exerts force, and consequently there is no pressure.

On the other hand, the relative pressure is always measured with respect to another that is taken as a reference, the most usual being the one exerted by the gaseous mass that surrounds the Earth: our atmosphere, since we are always subject to it.

For this reason, most of the instruments used to measure pressure, called *pressure gauges*are calibrated so that zero corresponds precisely to said atmospheric pressure.

Atmospheric pressure is defined as the force per unit area exerted by the Earth’s atmosphere, using the pascal as the unit of pressure measurement in the International System of SI measurements, both for atmospheric pressure and any other.

By using instruments such as a tire pressure gauge, for example, what we actually measure is the difference between the tire pressure and that exerted by the atmosphere. However, there are also instruments to measure absolute pressure, *barometers*.

Let Pab be the absolute pressure, Patm the standard atmospheric pressure (at sea level) and Pman (or in English Pgage) that measured by the manometer, the relationship between them is:

Pab = Patm + Pman

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**How is absolute pressure calculated?**

Since barometers are the instruments that measure absolute pressure, this is sometimes called *barometric pressure*. It is very easy to calculate it, even if you do not have a barometer, since it is enough to add the value of the standard atmospheric pressure to the manometric pressure.

It should be clarified that the atmospheric pressure varies according to the place on Earth where it is measured, since it is dependent on altitude, temperature and other climatic conditions. The standard value of the Patm in pascals is 101,325 Pa, and it is normal for it to vary in the range of approximately 96,000 to 105,000 Pa.

If any fluid has a manometric pressure of 65,000 Pa, let’s say, with respect to atmospheric pressure, this means that its absolute pressure is, according to the previous equation:

Pabs = 65000 + 101325 Pa = 166325 Pa.

**– Measurement of atmospheric pressure**

Atmospheric pressure is measured with a barometer, a device invented in 1643 by the Italian physicist and Galileo’s assistant, named Evangelista Torricelli (1608-1647).

In his famous experiment, Torricelli filled a tube with mercury, of a length greater than 762 mm and keeping one end open, he tipped it over an open container, also filled with mercury.

The scientist observed that the liquid column always rose to a certain height h, leaving a vacuum at the top, except for the presence of a small amount of mercury vapor.

Said height h is proportional to the pressure P at the base of the liquid column:

h= P/γHg

Where γHg is the specific weight of mercury, defined as weight per unit volume or also as the product of density times the acceleration of gravity g. The atmospheric pressure would be the sum of the vapor pressure of the mercury at the top of the tube and the pressure P, however the former is so small that in practice P coincides with Patm.

Thus:

h= Patm/γHg → Patm = γHg xh

Torricelli observed that the height of the column remained at 760 mm, and knowing that the density of mercury is 13600 kg/m3 and the acceleration of gravity is 9.91 m/s2, it is obtained that the atmospheric pressure is:

Patm = γHg xh = 13600 x 9.8 x 0.760 Pa = 101293 Pa.

**– Units for atmospheric pressure**

Other values for atmospheric pressure in different units are 1.013 bar = 1013 millibars = 14.70 lb/in2 (pounds per square inch or *psi*unit commonly used in English-speaking countries).

In addition, there is a unit that takes its value as a reference, called precisely *atmosphere*so that 1 atmosphere (abbreviated *atm*) is equal to 101293 Pa.

Atmospheric pressure can also be expressed directly in mm Hg, a unit now known as torr, after Evangelista Torricelli.

The height of the mercury column differs from place to place, therefore giving rise to different values of Patm. For example, in some Latin American cities, located at different altitudes above sea level:

-Mexico City: 585mm

-Caracas: 674 mm

-Bogotá: 560 mm

-La Paz: 490mm

**examples**

– Living beings on Earth are adapted to atmospheric pressure, which is an absolute pressure caused by the weight of the gases that make up the atmosphere. So although we don’t perceive it as a force on us, such pressure exists and is necessary to maintain life as we know it.

– The concept of absolute pressure is continually used when studying the earth’s climate and atmosphere, as well as in the design of barometers.

– Another example of the use of absolute pressure is in determining the height of aircraft using the altimeter. Since atmospheric pressure varies with height, it is not a good idea to make it a reference, so absolute pressure is used to ensure precision in measurements, which is very important for flight safety.

**solved exercises**

**– Exercise 1**

A manometer is connected to a chamber, giving a measurement of 24 kPa, in a place where the atmospheric pressure is 92 kPa. What is the absolute pressure in the chamber?

**Solution**

The data in the statement have the pressures in kPa or kilopascal. The pascal is a fairly small unit, so the prefixes kilo, mega, and giga are common. One kPa equals 1000 Pa, but since both data are in the same units, they can easily be added together and eventually converted to pascal if desired.

Using the equation: Pab = Patm + Pman and substituting values is:

Pab = 92 kPa + 24 kPa = 116 kPa = 116000 Pa

**– Exercise 2**

For most everyday applications, such as measuring tire pressure or engine compression, the reference pressure level 0 is taken to be atmospheric pressure.

So when a tire pressure gauge reads 32 psi, that’s relative pressure. What is the absolute pressure in the tire in this case?

**Solution**

The absolute pressure is the sum of the value thrown by the pressure gauge and the atmospheric pressure in the place. As stated before, the psi unit is commonly used in English-speaking countries.

Taking the standard value of 14.7 psi, the absolute pressure of the tire is:

Pabs = 32.0 psi + 14.7 psi = 46.7 psi 46.7 lb/in2

**References**

Cimbala, C. 2006. Fluid Mechanics, Fundamentals and Applications. Mc. Graw Hill.

Mott, R. 2006. Fluid Mechanics. 4th. Edition. Pearson Education.

Quora. What is absolute pressure? Retrieved from: quora.com

Smits, A. 2006. Fluid Mechanics, a physical introduction. Alpha Omega.

Streeter, V. 1999. Fluid Mechanics. McGraw Hill.

Zapata, F. Pressure and depth. Retrieved from: francesphysics.blogspot.com.