ATMOSPHERIC PRESSURE: NORMAL VALUE, HOW TO MEASURE IT, EXAMPLES - PHYSICAL - 2025

The atmospheric pressure is caused by the weight of the gases composing the atmosphere above the Earth. It is estimated that the mass of the atmosphere is about 5 x 10 ¹⁸ kg and all living beings are subject to the pressure that this mass exerts.

The first to measure it was the Italian scientist Evangelista Torricelli (1608-1647). He carried out a simple but very ingenious experiment in 1644: he completely filled a glass tube closed at one end with mercury, inverted it, and poured it into a container that also contained mercury.

Figure 1. Aneroid barometer to measure atmospheric pressure, unlike the mercury barometer, it does not contain liquid. Source: Wikimedia Commons.

Torricelli observed that the tube did not empty completely, but was filled with mercury to a height of 76 cm. Surprised, he did many tests with tubes of different shape, always obtaining the same result.

In this way, Torricelli realized that atmospheric pressure raised and kept the mercury column inside the tube at a height of 760 mm. In this way the average value of atmospheric pressure is established.

Since pressure is defined as force per unit area, the units of atmospheric pressure in the International System are newton / meter or pascal, which is abbreviated Pa. So in this system, atmospheric pressure P _atm has a value of:

This is the normal value of atmospheric pressure at 0 ºC and at sea level.

Atmospheric pressure at sea level and other variations

In theory, the maximum value of atmospheric pressure is just at sea level. Although there is so much variability at this level, experts need to set some reference system to help them determine its value.

Here are the main factors that affect the value of atmospheric pressure in a certain place on Earth:

-Altitude: for every 10 meters of height, the pressure decreases by 1 mm of Hg. But it also happens that the density of the gas that makes up the atmosphere is not constant. In principle, as the altitude increases, the density of the air decreases.

Figure 2. Altimeter, an instrument that measures altitude above sea level based on pressure changes. Source: Pixabay.

- Temperature: obviously the higher the temperature the density decreases and the air weighs less, therefore, the pressure value decreases.

- Latitude: atmospheric pressure is lower at equatorial latitudes, because the Earth is not a perfect sphere. The coast at the equator is farther from the center of the Earth than the poles and there the density of the air is also lower.

- Continentality: the more it moves towards the interior of the continents, the higher the atmospheric pressure, while in coastal places, the pressure is lower.

Variation of atmospheric pressure with height

The altimetric equation that relates the atmospheric pressure P of a place with its height z above sea level, has this form:

Here P _o is the existing pressure at the initial or reference height, which is normally taken at sea level, ρ _or the density of air at sea level and g the value of the acceleration of gravity. Later in the solved exercises section is the step-by-step deduction.

How is atmospheric pressure measured?

Atmospheric pressure is measured with the barometer. The simplest is like the one Torricelli built, based on mercury. The inclination of the tube or the diameter does not alter the height of the mercury column, unless the climatic factors are responsible for doing so.

For example, clouds form in regions of low pressure. So when the barometer reading drops, it's a sign that bad weather is coming.

Actually other liquids could also be used instead of mercury, for example a water barometer can be made. The problem is that the size of the column is 10.33 m, very impractical to be transported.

There are also instruments that measure pressure mechanically –through deformations in tubes or spirals-: aneroid barometers and manometers. They can measure the pressure difference between two points or also measure a pressure taking atmospheric pressure as a reference.

Units of pressure

The normal pressure value is used to define a new pressure unit: the atmosphere, abbreviated atm. Atmospheric pressure is 1 atm; in this way other pressures can be expressed in terms of atmospheric pressure, which is a very familiar value to all:

The following table shows the units most used in science and engineering to measure pressure, and the corresponding equivalent in pascals:

Unit	Equivalence in pascal
N / m 2	one
atm	101,355
mm Hg	133.3
lb / in 2	6894.76
Pub	1x 10 5

Hydrostatic, absolute and gauge pressure

On the free surface of a liquid in static equilibrium and open to the atmosphere, atmospheric pressure acts. But at the interior points of the liquid, of course the weight of the fluid column acts.

The weight of the column depends on its height and the density of the liquid, which we will assume constant, as does the temperature. In this case the pressure P is:

This is the hydrostatic pressure at any point inside a fluid with constant density and is directly proportional to the depth z of the fluid.

Regarding the absolute pressure P _abs in a fluid at rest, it is defined as the sum of the atmospheric pressure P _atm and the hydrostatic pressure P:

Finally, the gauge pressure P _man in a fluid at rest is the difference between the absolute and atmospheric pressure and in this case it is equivalent to measuring the hydrostatic pressure:

Examples

The force that the atmosphere exerts on the body

The magnitude of the total force exerted by the atmosphere on a human body can be estimated. Suppose that the body has approximately a surface area of ​​2 m ², since pressure is defined as force per unit area, we can solve for and calculate the force:

For this calculation we will use the normal value of atmospheric pressure that was established at the beginning:

This result is equivalent to more or less 20 tons of force, but it does not represent a problem for living beings that inhabit the surface of the Earth, who are adapted to this, just like the fish in the sea.

Although it is quite a large force. How come we don't collapse before it?

Well, the pressure inside the body equals the pressure outside. We do not collapse because the inward force is balanced by another outward force. But some people are affected by altitude and can bleed from the nose when climbing very high mountains. It is because the balance between blood pressure and atmospheric pressure has been disturbed.

Sip drinks with a straw or straw

Atmospheric pressure makes it possible to drink soda with a straw or straw. The Sumerians and other ancient cultures had discovered that they could drink beer using hollow plant stalks or reeds as straws.

Much later, in the late 19th and early 20th centuries, various models of straws were patented in the United States, including those with an accordion-shaped elbow, widely used today.

Figure 3. Atmospheric pressure allows you to sip with a straw. Source: Pixabay.

This is how they work: As the liquid is absorbed through the straw, the pressure above the liquid in the straw is reduced, causing the pressure below, which is higher, to push the liquid upwards for easy drinking.

For that reason, after extraction or dental surgery, it is not advisable to sip liquids in this way, as the decrease in pressure can cause the wound to open and begin to bleed.

Exercises

- Exercise 1

Derive the altimetric equation P (z):

-Po is the pressure at the reference level (sea level)

-z is the height

-ρ _o is the density of the fluid at sea level

-g is the value of the acceleration of gravity

Solution

First, let dp be a differential pressure, which according to the fundamental equation of hydrostatics is expressed as:

The minus sign takes into account the fact that pressure decreases with increasing z. Air will also be assumed to be an ideal gas, so pressure and density are related by:

The density is immediately substituted to obtain:

Now, writing pressure in this way assumes that the atmosphere is divided into layers of height dz, something like a stack of pancakes, each with pressure dp. In this way, a differential equation is obtained that is solved by separating the variables p and z:

It is then integrated on both sides, which is equivalent to adding the pressure contributions made by each layer. In the integral on the left it is made from a pressure P _or initial to a final pressure P. In the same way, the integral on the right evaluates from z _o to z:

The following is to solve for P using the exponential:

Finally, if both T and g are kept constant, ρ _o = (M / RT) P _o, then M / RT = ρ _o / P _o, and we can also make z _o = 0. Putting all this together:

- Exercise 2

What is the value of the atmospheric pressure in La Paz, Bolivia located at 3640 m above sea level? Take the mean air density as 1,225 kg / m ³ at sea level.

Solution

Simply substitute the numerical values ​​given in the altimetric equation:

In conclusion, it is about 66% of normal pressure.

References

1. Figueroa, D. (2005). Series: Physics for Science and Engineering. Volume 5. Fluids and Thermodynamics. Edited by Douglas Figueroa (USB).
2. Kirkpatrick, L. 2007. Physics: A Look at the World. 6th abridged edition. Cengage Learning.
3. The Standard Atmosphere. Recovered from: av8n.com
4. Sevilla University. Variation of atmospheric pressure. Recovered from: laplace.us.es.
5. Wikipedia. Hypsometric equation. Recovered from: es.wikipedia.org.
6. Wikipedia. Atmospheric pressure. Recovered from: es.wikipedia.org.