Absolute pressure, excess pressure, vacuum. Absolute vacuum and atmospheric pressure

According to the definition in physics, the concept of “vacuum” implies the absence of any substance and elements of matter in a certain space, in this case they speak of an absolute vacuum. A partial vacuum is observed when the density of the substance located in a given place in space is low. Let's take a closer look at this issue in the article.

Vacuum and pressure

In defining the concept of "absolute vacuum" we're talking about about the density of matter. It is known from physics that if gaseous matter is considered, then the density of the substance is directly proportional to pressure. In turn, when they talk about a partial vacuum, they mean that the density of matter particles in a given space is less than that for air at normal atmospheric pressure. That is why the question of vacuum is a question of pressure in the system under consideration.

In physics, absolute pressure is a quantity equal to the ratio of a force (measured in newtons (N)) that is applied perpendicularly to a certain surface to the area of that surface (measured in square meters), that is, P = F/S, where P is pressure, F is force, S is surface area. The unit of measurement for pressure is pascal (Pa), it turns out that 1 [Pa] = 1 [N]/ 1 [m 2 ].

Partial vacuum

It has been experimentally established that at a temperature of 20 °C on the surface of the Earth at sea level atmospheric pressure is 101,325 Pa. This pressure is called the 1st atmosphere (atm.). Approximately we can say that the pressure is 1 atm. equals 0.1 MPa. Answering the question of how much we make up the corresponding proportion and find that 1 Pa = 10 -5 atm. A partial vacuum corresponds to any pressure in the space under consideration that is less than 1 atm.

If we translate the indicated figures from the language of pressure into the language of the number of particles, then it should be said that at 1 atm. 1 m 3 of air contains approximately 10 25 molecules. Any decrease in this value leads to the formation of a partial vacuum.

Vacuum measurement

The most common instrument for measuring small vacuums is a conventional barometer, which can only be used in cases where the gas pressure is several tens of percent of atmospheric pressure.

To measure higher vacuum values use electrical diagram with Wheatstone Bridge. The idea of use is to measure the resistance of the sensing element, which depends on the concentration of molecules in the gas surrounding it. The greater this concentration, the more molecules hit the sensitive element, and the more heat it transfers to them, this leads to a decrease in the temperature of the element, which affects its electrical resistance. This device can measure vacuum with pressures of 0.001 atm.

Historical background

It is interesting to note that the concept of "absolute vacuum" was completely rejected by famous ancient Greek philosophers, such as Aristotle. In addition, the existence of atmospheric pressure was not known until the beginning of the 17th century. Only with the advent of modern times experiments began to be carried out with tubes filled with water and mercury, which showed that the earth's atmosphere exerts pressure on all surrounding bodies. In particular, in 1648, Blaise Pascal was able to measure pressure at an altitude of 1000 meters above sea level using a mercury barometer. The measured value turned out to be much lower than at sea level, thereby the scientist proved the existence of atmospheric pressure.

The first experiment that clearly demonstrated the power of atmospheric pressure and also emphasized the concept of vacuum was carried out in Germany in 1654, now known as the Magdeburg Spheres Experiment. In 1654, German physicist Otto von Guericke was able to tightly connect two metal hemispheres with a diameter of only 30 cm, and then pumped the air out of the resulting structure, thereby creating a partial vacuum. History tells that two teams of 8 horses each, pulling in opposite directions, were unable to separate these spheres.

Absolute vacuum: does it exist?

In other words, is there a place in space that does not contain any matter? Modern technologies allow you to create a vacuum of 10 -10 Pa or even less, however, this absolute pressure does not mean that there are no particles of matter remaining in the system under consideration.

Let us now turn to the most empty space in the Universe - to open space. What is the pressure in the vacuum of space? Pressure in outer space around the Earth is 10 -8 Pa, at this pressure there are about 2 million molecules in a volume of 1 cm 3. If we talk about intergalactic space, then according to scientists, even in it there is at least 1 atom in a volume of 1 cm 3. Moreover, our Universe is permeated with electromagnetic radiation, the carriers of which are photons. Electromagnetic radiation- this is energy that can be converted into the corresponding mass according to Einstein’s famous formula (E = m*c 2), that is, energy, along with matter, is a state of matter. From this it follows that an absolute vacuum does not exist in the Universe known to us.

When choosing a vacuum pump (or compressor) and assessing its suitability for use in a particular technology, two main characteristics are used:

PRESSURE
PERFORMANCE

The vacuum pump or compressor that a potential user is looking for must, first of all, provide the required level of pressure. Then the task is to obtain this pressure in a certain period of time. The speed at which the set pressure value is obtained is determined by the pumping speed of the vacuum pump. In this case, gas compressors pump gases and create pressures above atmospheric. Vacuum pumps generate pressures below atmospheric, i.e. create a vacuum.

This article will talk about low pressure, i.e. about VACUUM as the main technical specifications all vacuum pumps. The creation or generation of a vacuum by a device is a dynamic process of lowering atmospheric pressure in volume and time. When searching for and selecting a vacuum pump based on vacuum level, they usually talk about two characteristics of a vacuum pump related to pressure:

ultimate residual pressure (or ultimate vacuum, ultimate pressure)
working pressure (or working vacuum, working pressure)

Limit residual pressure - this is the best (highest) vacuum value that the design of this vacuum pump can achieve. It is important to understand that when the vacuum pump reaches this limit value vacuum, the gas pumping performance becomes zero, i.e. pumping stops, and in the future, when the pump operates, this value of the maximum pressure will be maintained as a certain achieved equilibrium state of the “pump-pumped-out volume” system.

As a rule, the value of the maximum residual pressure is achieved only when the vacuum pump operates in the “self-propelled” mode, i.e. with the inlet pipe plugged. This can be explained quite simply: when technological volumes (containers, pipelines, joints, chambers, etc.) are connected to the pump, there are always leaks (leaks) or gas desorption phenomena that do not allow the pumped volume to achieve the maximum vacuum value that the pump itself can create .

Working pressure - this is a given vacuum value that must be provided and maintained by a vacuum pump in a particular technology or process.

When choosing a vacuum pump, its maximum residual pressure should be slightly better than the operating pressure. This seems to provide a certain “margin of safety”, i.e. guarantee that the pressure required in the process will be achieved using this particular vacuum pump.

2. Gas pressure in the volume. Atmospheric pressure. The concept of "VACUUM".

The pressure of gases in a closed volume is the total force exerted by impacts (pushes) of constantly moving gas molecules into the walls of the volume, as a result of their constant Brownian motion and collision with each other and with the solid walls of the vessel.

The basic SI unit of pressure is "Pa" (Pascal):

1 Pa = 1 N/m2 = 0.01 mbar [1]

Other generally accepted pressure units and their relationships are shown in Table 1:

Table 1
Pressure unit	bar	mbar	mm. Hg Art.	m water Art.	Pa	kPa	MPa	atm.	at.	kgf/cm 2	psi
Bar	1	1000	750	10,2	100 000	100	0,1	0,9869	1,02	1,02	14,5

Atmospheric pressure - this is the pressure exerted by the mass of the air column, as a mixture of gases, extending to a height of more than 1000 km from the surface of the earth and ocean. It must be understood that the higher the point of measurement of this atmospheric pressure is from the sea surface, the less concentrated the atmosphere, the rarer the mixture of gases (as if their mass is diluted in a huge volume increasing with height) and, as a result, the pressure of this mixture of gases drops with rise to height (see Fig. 2). Why? It’s just that the planet Earth has been tripled for a long time, around which there is an atmosphere, like a gas aura around a ball. Thanks to this atmospheric aura, organisms live and the most vital reactions of substances occur, constantly consuming oxygen, and plants, which constantly produce this oxygen and restore the so-called. atmospheric oxygen balance. The most vivid examples- this is wind, combustion (as a process of oxidation) and respiration of living organisms, animals, people.

The curve of changes in atmospheric pressure up to an altitude of 12 km above sea level is shown in Fig. 3.

Earth's atmosphere . It is generally accepted that this is a mixture of 14 main “earthly” gases (see Fig. 1), of which three make up the lion’s share, in total more than 99% (nitrogen - more than 78%, oxygen - more than 20%, water vapor may be more 1%).

The earth's atmosphere is divided into zones based on pressure and temperature parameters: the troposphere, stratosphere, mesosphere and thermosphere (see Fig. 4).

Vacuum - this is any pressure whose value is below atmospheric. Normal atmospheric pressure in terrestrial conditions is considered to be the absolute pressure of the atmospheric column at the surface level of the world's oceans (sea). This value is 1013 mbar abs. "abs." - here we mean absolute pressure, which is equal to zero in the case when there is not a single gas molecule in the volume. Because on the surface of the earth, in its bowels and in the atmosphere there is always gaseous substances and vapors of liquid substances, then absolute vacuum is unattainable under terrestrial conditions. No matter how quickly and well the volumes are pumped out by modern vacuum pumps, no matter how sealed they are, in the microscopic roughness of the walls of the volumes there is always a certain amount of gas molecules that cannot be removed from these microreliefs. In addition, when there is pressure on the walls of vessels from the outside, there are always gas molecules that slip through, as if seeping through a sieve, inside, even through solid crystal lattices metals In closed volumes there are always phenomena of gas desorption, i.e. release of gas molecules from the walls of the volume inwards, there are always micropores and microcracks through which gases penetrate into the zones low pressure. All this does not allow us to obtain an absolute vacuum under terrestrial conditions.

Facts: The Alps are a mountain range that crosses the borders of six countries. In their very heart rises the famous Mont Blanc mountain, located on the border of France and Italy.

The Alps themselves are a mountain range that stretches across Europe for almost 1,200 km; at its widest point between the Italian Verona and the German Garmisch-Partenkirchen, it is about 260 km wide, occupying a total area of 190 thousand square meters. km. The Alps are located entirely or partially on the territory of 8 countries. By share total area states in the Alps, these countries are located as follows: Liechtenstein (100%), Monaco (100%), Austria (65%), Switzerland (60%), Slovenia (40%), Italy (17%), France ( 7%), Germany (3%).

Facts: Everest, also known as Chomolungma, is the highest peak in the world, the height of this mountain is 8848 meters. Everest is located in the Himalayan Mountains, which stretch across the Tibetan Plateau and the Indo-Gangetic Plain in the territory of several countries: Nepal, India, Bhutan, China.

The summit of Everest is located in China, but the mountain itself is located on the China-Nepal border.

Facts: In civil and military aviation It is very important to maintain atmospheric pressure inside the aircraft, because... when it is raised to any height from the surface of the Earth, the pressure outside drops, and this entails an outflow of air from the aircraft cabin into external environment. To prevent this from happening, two basic conditions for a normal flight with the pilot or passengers inside must be met:

The aircraft body must be sealed (maximum no air leaks to the outside);
- air must be supplied into the housing by compressors under excess pressure in order to compensate for the always existing leaks and micro leaks of air to the outside.

If in military aircraft it is possible to solve the problem of leaks using individual pilot masks, then in civil aircraft, where there are many passengers, special ones are created. automated systems maintaining atmospheric pressure.

Rice. 3. Graph of decrease in atmospheric pressure with altitude above sea level (from 0 to 12) km.

Rice. 4. Diagram of air temperature distribution in 4 layers of the atmospheric column:
troposphere(up to 11 km), stratosphere(from 11 to 47 km), mesosphere(from 47 to 80 km), thermosphere(over 80 km).

3. Vacuum depth gradation (technical vacuum levels).

There are several methods for dividing the entire possible low pressure scale into various intervals (segments). The most common are academic graduation and industrial graduation.

Academic is based on assessing the density (degree of rarefaction) of gases by the nature of the movement of their molecules in volumes by measuring the path lengths of molecules between their collisions with each other and with the walls of vessels, i.e. so-called commensurate free path lengths. The more average length free path of the molecule, the better the vacuum. So, for example, if a gas molecule in a volume manages to fly from wall to wall without colliding with other molecules, then this is an indicator that an ultra-high vacuum has been achieved in such a volume.

Since we specialize in the supply of equipment for industrial applications, in this article we will consider an industrial approach to dividing vacuum into 4 classes (intervals). This method complies with the European standard DIN 28400. The vacuum classes are given in Table 2.

Table 2
Technical vacuum levels (classes)	Pressure range
FOREVACUUM (rough vacuum)	(1000 to 1) mbar abs.
MEDIUM VACUUM (fine vacuum)	(from 1 to 10 -3) mbar abs.
HIGH VACUUM	(from 10 -3 to 10 -7) mbar abs.
Ultrahigh vacuum	(10 -7 and below) mbar abs.

4. Basic laws of GAS PHYSICS and the equation of state of an ideal gas.

Boyle-Marriott law.

The Boyle-Mariotte law was established by the English physicist Robert Boyle in 1662 and independently by the French scientist Edme Mariotte in 1679 and sounds like this:

For a given mass of gas at a constant temperature, the product of its pressure is p per volume V there is a constant value:

PV = const [ 2 ]

This law is also called the LAW OF ISOTHERMAL PROCESS.

As an example:

When the volume of a certain amount of gas gradually increases, in order to keep its temperature constant, the gas pressure must also gradually decrease.

Gay-Lussac's law.

Law relating gas volume V and its temperature T, was established by the French scientist Joseph Gay-Lussac in 1802.

For a given mass of gas at constant pressure, the ratio of the volume of the gas to its temperature is a constant value.

VT = const [ 3 ]

This law is also called the LAW OF ISOBAR PROCESS.

As an example:

When a certain amount of gas is gradually heated, in order to keep the pressure constant, the gas must also gradually expand.

Charles's law.

Law relating gas pressure p and its temperature T, installed by Jacques Charles in 1787.

For a given mass of gas in a closed, sealed volume, the gas pressure is always directly proportional to its temperature.

PT = const [ 4 ]

This law is also called the LAW OF ISOCHORIC PROCESS.

As an example:

When a certain amount of gas is gradually heated in a closed volume, its pressure will also gradually increase.

Equation of state of an ideal gas.

The equation that allows us to generalize all three basic gas laws of thermodynamics is called the ideal gas equation of state or the Mendeleev-Clapeyron equation. It gives the relationship between the three most important macroscopic parameters that describe the state of an ideal gas: pressure p, volume V, temperature T, and has the form:

[ 5 ]

p∗V	= Const = f, where f depends on the type of gas
T

or when written in another form: [ 6 ]

p ∗ V =	m	∗R∗T
	μ

p- gas pressure, Pa(N/m 2)

V- volume of gas, m 3

m- gas mass, kg

μ - molar mass gas

R = 8.31 J/mol ∗ K- universal gas constant,

T- gas temperature, °K(degrees absolute scale Kelvin).

Under ideal gas refers to a gas whose particles do not interact at a distance material points and experience absolutely elastic collisions with each other and with the walls of blood vessels.

It is important to understand that everything gas laws work for a fixed mass (quantity) of gas.

These laws work well for vacuum regimes and are not acceptable under very high pressures and temperatures.

5. Design types of vacuum pumps.

If we talk about the vacuum level and its use for industrial and research purposes, then:

In mass global industry, forevacuum and medium vacuum are very widely used;

In rarer high technologies, forevacuum, medium and high vacuum are used;

In laboratories and research you can find all classes of vacuum, incl. and super high.

To obtain all classes in industry they use various designs vacuum pumps, the main types of which are shown in Table 3.

Table 3
Pump type	Structural view (scheme)	Operating pressure range
Diaphragm Vacuum Pump: 1 pumping stage - 2 pumping stages - 3 pumping stages - 4 pumping stages		Accordingly, work in the range: From 100 mbar abs. up to atmospheric pressure - from 10 mbar abs. up to atmospheric pressure - from 2 mbar abs. up to atmospheric pressure - from 0.5 mbar abs. up to atmospheric pressure
Vortex blower		from 600 mbar abs. up to atmospheric pressure
Double rotor blower		from 400 mbar abs. up to atmospheric pressure
Dry vane rotor vacuum pump		from 150 mbar abs. up to atmospheric pressure
Water ring vacuum pump		from 33 mbar abs. up to atmospheric pressure
Dry Cam Vacuum Pump		from 20 mbar abs. up to atmospheric pressure
Rotary vane vacuum pump with recirculating lubrication		from 0.5 mbar abs. up to atmospheric pressure
Dry Scroll Vacuum Pump
Dry Screw Vacuum Pump		from 0.01 mbar abs. up to atmospheric pressure
2 Stage Oil Bath Rotary Vane Vacuum Pump		from 0.0005 mbar abs. up to atmospheric pressure
Roots dry vacuum pump (booster)		from 0.001 to 25 mbar abs.
High vacuum pumps: Turbomolecular - diffusion steam-oil - cryogenic - magnetic discharge - sorption, ionic and heteroionic		from 10 -11 to 5 mbar abs.

In this section, the main emphasis is on pumps for obtaining fore-vacuum, because... This is the most popular niche in the vacuum equipment market, and not only in Russia and the CIS countries, but throughout the world.

You should also know that high-vacuum pumps cannot operate without for- and medium-vacuum vacuum pumps, because they start working only with low pressure(as a rule, from a medium vacuum) and their exhaust must occur in the vacuum zone, otherwise high and ultra-high vacuum are unattainable. That. foreline and medium vacuum pumps are in demand in all industries, high-tech areas and scientific research.

The concept of vacuum has changed over time. At the very beginning of the development of sciences about the surrounding world, vacuum simply meant emptiness; even vacuum itself is translated from Latin as “emptiness.” It was more of a philosophical category, since scientists did not have the opportunity to study anything even remotely consistent with ideas about vacuum. The modern one calls vacuum the state of a quantum field in which it energy state is at its lowest level. This state is characterized primarily by the fact that there are no real particles in it. Technical vacuum is a highly rarefied gas. This is not quite an ideal vacuum, but the fact is that under the conditions it is unattainable. After all, all materials allow gases to pass through in microscopic volumes, so any vacuum contained in a vessel will have interference. The degree of its rarefaction is measured using the parameter λ (lambda), which indicates the length of the free particle. This is the distance that it can travel before colliding with an obstacle in the form of another particle or the wall of a container. A high vacuum is one in which gas molecules can pass from one wall to another without almost ever colliding with each other. Low vacuum is characterized by sufficient a large number collisions. But even if we assume that it is possible to achieve the ideal, we still should not forget about such a factor as thermal radiation - the so-called photon gas. Thanks to this phenomenon, the temperature of a body placed in a vacuum would, after some time, become the same as the walls of the vessel. This will happen precisely due to the movement of thermal photons. A physical vacuum is a space in which there is no mass at all. But, according to quantum field theory, even in this state it cannot be called absolute emptiness, since virtual particles are continuously being formed in the physical vacuum. They are also called zero-point field oscillations. There are various field theories, according to which the properties of massless space may vary slightly. It is assumed that the vacuum can be one of several types, each of which has its own characteristics. Some of the properties of the quantum field that were predicted by theoretical scientists have already been confirmed experimentally. Among the hypotheses there are also those that can confirm or refute the fundamental theories of physics. For example, the assumption that so-called false vacua (various vacuum states) are possible is very important for confirming the Bolshoi inflation theory.

The term " vacuum", How physical phenomenon- an environment in which the gas pressure is below atmospheric pressure.

Quantitative characteristics The vacuum is absolute pressure. The basic unit of pressure measurement in International system(SI) is Pascal (1 Pa = 1N/m2). However, in practice there are also other units of measurement, such as millibars (1 mbar = 100 Pa) and Torres or millimeters mercury(1 mmHg = 133.322 Pa). These units are not SI units, but are acceptable for measuring blood pressure.

Vacuum levels

Depending on how much the pressure is below atmospheric (101325 Pa), various phenomena, as a result of which various means can be used to obtain and measure such pressure. Nowadays, there are several levels of vacuum, each of which has its own designation in accordance with the intervals of pressure below atmospheric:

Low vacuum (LV): from 10 5 to 10 2 Pa,
Medium vacuum (SV): from 10 2 to 10 -1 Pa,
High vacuum (HV): from 10 -1 to 10 -5 Pa,
Ultra-high vacuum (UHV): from 10 -5 to 10 -9 Pa,
Extremely high vacuum (EHV):

These vacuum levels are divided into three production groups depending on the area of application.

- Low vacuum: Mainly used where large amounts of air need to be pumped out. To obtain low vacuum, electromechanical pumps of vane type, centrifugal, side channel pumps, flow generators, etc. are used.

Low vacuum is used, for example, in silk-screen printing factories.

- Industrial vacuum: The term “industrial vacuum” corresponds to a vacuum level from -20 to -99 kPa. This range is used in most applications. Industrial vacuum is obtained using rotary, liquid ring, piston pumps and vane vacuum generators according to the Venturi principle. Industrial vacuum applications include suction cup gripping, thermoforming, vacuum clamping, vacuum packaging, etc.

- Technical vacuum: corresponds to vacuum level from -99 kPa. This level of vacuum is obtained using two-stage rotary pumps, eccentric rotary pumps, Roots vacuum pumps, turbomolecular pumps, diffusion pumps, cryogenic pumps, etc.

This level of vacuum is used mainly in lyophilization, metallization and heat treatment. In science, technical vacuum is used as a simulation of outer space.

The highest vacuum value on earth is significantly less than value absolute vacuum, which remains a purely theoretical value. In fact, even in space, despite the absence of an atmosphere, there is no large number atoms.

The main impetus for the development of vacuum technology came from research in the industrial field. There are currently a large number of applications in various sectors. Vacuum is used in electroray tubes, incandescent lamps, particle accelerators, metallurgy, food and aerospace, nuclear fusion control, microelectronics, glass and ceramics, science, industrial robotics, suction cup gripping systems etc.

Examples of vacuum applications in industry

Vacuum multiple gripping systems "OCTOPUS"

Vacuum suction cups - general information

Vacuum suction cups are an indispensable tool for gripping, lifting and moving objects, sheets and various objects that are difficult to move with conventional systems due to their fragility or risk of deformation.

When used correctly, suction cups provide convenient, economical and safe operation, which is a fundamental principle for the ideal implementation of automation projects in production.

Long-term research and attention to the requirements of our customers have allowed us to produce suction cups that can withstand high and low temperatures, abrasive wear, electrostatic discharges, aggressive environments, and also do not leave stains on the surface of carried objects. In addition, the suction cups comply with EEC safety standards and FDA, BGA, TSCA food standards.

All suction cups are made from high quality vacuum formed components and are treated with anti-corrosion treatment for long service life. Regardless of the configuration, all suction cups have their own markings.

Octopus multiple capture system

The numerical value of pressure is determined not only by the adopted system of units, but also by the selected reference point. Historically, three pressure reference systems have developed: absolute, excess and vacuum (Fig. 2.2).

Rice. 2.2. Pressure scales. Relationship between pressure

absolute, excess and vacuum

Absolute pressure measured from absolute zero (Fig. 2.2). This system is at atmospheric pressure. Therefore, the absolute pressure is

Absolute pressure is always a positive value.

Overpressure measured from atmospheric pressure, i.e. from conditional zero. To move from absolute to excess pressure, it is necessary to subtract atmospheric pressure from absolute pressure, which in approximate calculations can be taken equal to 1 at:

Sometimes excess pressure is called gauge pressure.

Vacuum pressure or vacuum called lack of pressure to atmospheric

Excess pressure indicates either excess above atmospheric pressure or deficiency below atmospheric pressure. It is clear that vacuum can be represented as negative excess pressure

As can be seen, these three pressure scales differ from each other either in the beginning or in the direction of the counting, although the counting itself can be carried out in the same system of units. If pressure is determined in technical atmospheres, then the designation of the pressure unit ( at) another letter is assigned, depending on what pressure is taken to be “zero” and in what direction the positive count is being made.

For example:

The absolute pressure is 1.5 kg/cm2;

Excess pressure is 0.5 kg/cm2;

The vacuum is 0.1 kg/cm2.

Most often, an engineer is not interested in absolute pressure, but in its difference from atmospheric pressure, since the walls of structures (tank, pipeline, etc.) usually experience the difference between these pressures. Therefore, in most cases, instruments for measuring pressure (pressure gauges, vacuum gauges) directly indicate excess (gauge) pressure or vacuum.

Units of pressure. As follows from the very definition of pressure, its dimension coincides with the dimension of stress, i.e. represents the dimension of force divided by the dimension of area.

The unit of pressure in the International System of Units (SI) is the pascal - the pressure caused by a force uniformly distributed over an area normal to it, i.e. Along with this unit of pressure, enlarged units are used: kilopascal (kPa) and megapascal (MPa) :

In technology, in some cases, the technical MKGSS (meter, kilogram-force, second, a) and physical GHS (centimeter, gram, second) systems of units continue to be used. Non-system units are also used - technical atmosphere and bar:

You should also not confuse the technical atmosphere with the physical atmosphere, which is still somewhat common as a unit of pressure:

2.1.3. Properties of hydrostatic pressure

Hydrostatic pressure has two main properties.

1st property. The forces of hydrostatic pressure in a fluid at rest are always directed inward along the normal to the area of action, i.e. are compressive.

This property can be proven by contradiction. If we assume that the forces are directed normally outward, then this is equivalent to the appearance of tensile stresses in the liquid, which it cannot perceive (this follows from the properties of the liquid).

2nd property. The magnitude of hydrostatic pressure at any point in the liquid is the same in all directions, i.e. does not depend on the orientation in space of the site on which it acts

where are hydrostatic pressures in the direction of the coordinate axes;

The same in any direction.

To prove this property, let us select an elementary volume in a stationary liquid in the form of a tetrahedron with edges parallel to the coordinate axes and correspondingly equal to , And (Fig. 2.3).

Rice. 2.3. Scheme to prove the property

on the independence of hydrostatic pressure from direction

Let us introduce the following notation: - hydrostatic pressure acting on a face normal to the axis;

Pressure on the face normal to the axis;

Pressure acting on an inclined face;

The area of this face;

Liquid density.

Let us write down the equilibrium conditions for the tetrahedron (as for solid) in the form of three force projection equations and three moment equations:

When the volume of the tetrahedron decreases to zero in the limit, the system of acting forces is transformed into a system of forces passing through one point, and, thus, the moment equations lose their meaning.

Thus, inside the selected volume, a unit mass force acts on the liquid, the acceleration projections of which are equal to , , And . In hydraulics, it is customary to relate mass forces to a unit of mass, and since , the projection of a unit mass force will be numerically equal to acceleration.

where ,, are the projections of a unit mass force on the coordinate axes;

Mass of liquid;

Acceleration.

Let's create an equilibrium equation for the selected volume of liquid in the direction of the axis , taking into account that all forces are directed along the normals to the corresponding areas inside the volume of liquid:

where is the projection of force from hydrostatic pressure;

Projection of force from pressure;