Let us consider the equilibrium of a homogeneous fluid located in the gravitational field of the Earth.
Each particle of liquid located in the gravitational field of the Earth is affected by the force of gravity. Under the influence of this force, each layer of liquid presses on the layers located underneath it. As a result, the pressure inside the liquid at different levels will not be the same. Therefore, in liquids there is pressure due to its weight.
The pressure due to the weight of the liquid is called hydrostatic pressure.
For a quantitative calculation, let us mentally isolate a small cylindrical volume in the liquid, located vertically, with a cross-section S and height h(Fig. 2). In the case of a stationary fluid, the weight of this cylinder, and therefore the force of pressure on the platform S at the base will be equal to the force of gravity \(~m \vec g\).
Then the pressure on the site
\(~p = \frac(mg)(S) = \frac(\rho Vg)(S) = \frac(\rho hSg)(S) = \rho gh.\)
\(~p = \rho gh\) - hydrostatic pressure, Where ρ - liquid density, h- height of the liquid column. Thus, hydrostatic pressure is equal to the weight of a liquid column with a unit base and a height equal to the immersion depth of a point under the free surface of the liquid.
Graphically, the dependence of pressure on the depth of immersion in liquid is presented in Figure 3.
The pressure of the liquid at the bottom does not depend on the shape of the vessel, but is determined only by the height of the liquid level and its density. In all cases shown in Figure 4, the liquid pressure at the bottom of the vessels is the same.
At a given depth, liquid presses equally in all directions - not only down, but also up and to the sides.
Consequently, the pressure on the wall at a given depth will be the same as the pressure on a horizontal platform located at the same depth.
If pressure is created above the free surface of the liquid p 0 then the pressure in the liquid at depth will be
\(~p = p_0 + \rho gh.\)
Pay attention to the difference in expressions: “fluid pressure at depth h" (p = pgh) and "pressure in the liquid at depth h" (p = p 0 + pgh). This must be taken into account when solving various problems.
The pressure forces on the bottom and walls can be calculated using the formulas\[~F_d = \rho gh S_d\] - the force of liquid pressure on the horizontal bottom, where S d - bottom area;
\(~F_(st) = \frac(\rho gh)(2) S_(st)\) is the force of liquid pressure on the lateral rectangular vertical wall of the vessel, where S st - wall area.
In a fluid at rest, the free surface of the fluid is always horizontal.
There are often cases when a liquid, at rest relative to a vessel, moves with it. If the vessel moves uniformly and rectilinearly, then the free surface of the liquid will be horizontal. But if the vessel moves with acceleration, then the situation changes and questions arise about the shape of the free surface of the liquid and the distribution of pressure in it.
Thus, in the case of horizontal motion of a vessel with acceleration \(~\vec a\) in the gravitational field of the Earth, any part of the liquid with a mass m moves with the same acceleration \(~\vec a\) under the action of the resultant pressure force \(~\vec N_d\) acting from the rest of the fluid and gravity \(~m \vec g\) (Fig. 5).
Basic equation of dynamics:
\(~\vec N_d + m \vec g = m \vec a.\)
As a result, the free surface of the liquid will not be horizontal, but forms an angle with the horizon α , which can be easily found if we project the basic equation of dynamics onto the horizontal and vertical axes\[~N_d \sin \alpha = ma; \N_d\cos\alpha = mg\]. From here
\(~\operatorname(tg) = \frac ag.\)
The pressure on the horizontal surface (horizontal bottom) will increase in the direction opposite to the acceleration.
Literature
Aksenovich L. A. Physics in secondary school: Theory. Tasks. Tests: Textbook. allowance for institutions providing general education. environment, education / L. A. Aksenovich, N. N. Rakina, K. S. Farino; Ed. K. S. Farino. - Mn.: Adukatsiya i vyakhavanne, 2004. - P. 95-97.
There are legends that sunken ships in the ocean do not sink to the bottom, but hang at some depth, traveling along with ocean currents. Is this fair? Water pressure in the depths of the ocean really reaches enormous values. At a depth of 10 m it presses with a force of 10 N per 1 cm 2 of a submerged body, at a depth of 100 m - 0.1 kN, 1,000 m - 1 kN, etc. At the depth of the Mariana Trench - 11.5 km - the water pressure reaches almost 120 MPa. With such pressure in the depths of the ocean, pieces of wood, after being brought to the surface, were so compressed that they sank in the water, and tightly sealed bottles were crushed by the pressure of the water. There is an opinion that a firearm lowered to such a depth cannot be fired.
It can be assumed that the monstrous pressure of water in the depths of the ocean will compact the water so much that ships and other heavy objects will hang in it and will not sink. But water, like all liquids, is difficult to compress. If you compressed water to such a density that it would float in it, it would be necessary to compress it 8 times. Meanwhile, to compact only in half, that is, reduce the volume by half, a pressure of 1100 MPa is required. This corresponds to a depth of 110 km, which is not realistic!
At the deepest point of the ocean, the water is 5% denser. This can hardly affect the conditions of floating of various bodies in it, especially since solid objects immersed in such water are also subject to this pressure and, therefore, also become compacted. Therefore, we can conclude that they rest on the ocean floor. There is no chance even for ships turned upside down, despite the fact that in some rooms of the ship the air will be tightly locked. Is it possible that some of them never reach the bottom, remaining suspended in the dark depths of the ocean? A slight push would be enough to throw such a vessel off balance, turn it over, fill it with water and force it to fall to the bottom. But where do shocks come from in the depths of the ocean, where silence and calm always reign and where even the echoes of storms do not penetrate?
All these arguments are based on a physical error. A ship with its keel upturned will not begin to sink at all, but will remain on the surface of the water. There is no way he can find himself halfway between the ocean level and its bottom.
In view of the fact that such a phenomenon has never been observed or tested with sunken ships, a serious scientist should leave even the slightest doubt about anything. Moreover, the opinion about frozen ships is shared by many sailors. The fact is that ships often have sealed compartments. And if these compartments are not damaged and there is air left in them, then the pressure of water in the depths of the ocean does not compress it, and it remains the same volume. Therefore, the ship, having an overall density higher than the surface density of ocean water (almost always less dense - due to both higher temperature and lower salinity), begins to sink, and when it reaches cold temperatures (in the depths of the oceans the temperature is +4 0 C, while its density maximum) and its more salty layers, hangs for an indefinite time...
It turns out that by breaking a vessel on the side when launching it, we thereby seal its fate. She relentlessly leads him through the seas and oceans where he is destined to visit. And if it happens that the ship sinks, this is not the end. Water pressure in the depths of the ocean may give rise to a new legend about wandering, suspended sunken ships!
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In § 147 it was stated that the pressure of a water column 10 meters high is equal to one atmosphere. The density of sea salt water is 1-2% greater than the density of fresh water. Therefore, we can assume with reasonable accuracy that for every 10 meters of immersion in the sea, hydrostatic pressure increases by one atmosphere. For example, a submarine submerged 100 m under water experiences a pressure of 10 atm (above atmospheric pressure), which approximately corresponds to the pressure inside the steam boiler of a steam locomotive. Thus, each depth below the surface of the water corresponds to a certain hydrostatic pressure. Submarines are equipped with pressure gauges that measure seawater pressure; this allows you to determine the depth of the dive.
At very great depths, the compressibility of water begins to be noticeable: due to compression, the density of water in deep layers is greater than on the surface, and therefore pressure increases with depth somewhat faster than according to a linear law, and the pressure graph deviates somewhat from a straight line. The added pressure caused by the compression of water increases in proportion to the square of the depth. At the greatest depth of the ocean, equal to 11 km, it reaches almost 3% of the total pressure at this depth.
To explore very great depths, bathyspheres and bathyscaphes are used. A bathysphere is a hollow steel ball that can withstand the enormous pressure of water in the depths of the sea. Portholes are installed in the wall of the bathysphere - holes hermetically sealed with durable glass. The spotlight illuminates layers of water where sunlight can no longer penetrate. The bathysphere, which houses the researcher, is lowered from the ship on a steel cable. In this way, it was possible to reach depths of about 1 km. Bathyscaphes, consisting of a bathysphere, which is fixed at the bottom of a large steel tank filled with gasoline (Fig. 254), descend to even greater depths.
Rice. 254. Bathyscaphe
Since gasoline is lighter than water, such a bathyscaphe can float in the depths of the sea like an airship in the air. Gasoline plays the role of light gas here. The bathyscaphe is equipped with a supply of ballast and engines, with the help of which it, unlike the bathysphere, can move independently without being connected to the ship on the surface of the water.
At first, the bathyscaphe floats on the surface of the water, like a surfaced submarine. To dive into the empty ballast compartments, seawater is let in, and the bathyscaphe goes under the water, sinking deeper and deeper, to the very bottom. To ascend, the ballast is dumped and the lightweight bathyscaphe floats to the surface again. The deepest dive was made on January 23, 1960, when the bathyscaphe lay for 20 minutes at the bottom of the Mariana Trench in the Pacific Ocean, at a depth of 10919 m below the surface of the water, where the water pressure (calculated taking into account the increase in water density due to salinity and due to compression) was over 1150 atm. Researchers descending into the submersible discovered living beings even at this greatest depth of the world's oceans.
A swimmer or scuba diver who dives under water experiences the hydrostatic pressure of the surrounding water over the entire surface of his body in excess of the constant atmospheric pressure. Although the body of a diver (Fig. 255), working in a rubber suit (spacesuit), is not in direct contact with the water, it experiences the same pressure as the swimmer’s body, since the air in the spacesuit must be compressed to the pressure of the surrounding water. For the same reason, the air supplied through the hose to the diver for breathing must be pumped under a pressure equal to the water pressure at the depth of the diver's immersion. The air coming from compressed air cylinders into the scuba diver’s mask should have the same pressure. Underwater you have to breathe high pressure air.
Rice. 255. Diver in a rubber suit with a metal helmet. Air is supplied to the diver through a tube
Rice. 256. Diving bell
The diving bell (Fig. 256) or the caisson does not save the submariner from high pressure, since the air in them must be compressed enough to prevent water from entering the bell, i.e., to the pressure of the surrounding water. Therefore, when the bell is gradually immersed, air is constantly pumped into it so that the air pressure is equal to the water pressure at a given depth. Increased pressure is harmful to human health, and this sets a limit to the depth at which a diver can safely work. The usual diving depth of a diver in a rubber spacesuit does not exceed 40 m: at this depth the pressure is increased by 4 atm. A diver’s work at greater depths is only possible in a hard (“shell”) suit that absorbs water pressure. In such a spacesuit you can safely stay at a depth of up to 200 m. The air in such a spacesuit is supplied at atmospheric pressure.
During a prolonged stay under water at a pressure significantly higher than atmospheric pressure, a large amount of air becomes dissolved in the blood and other body fluids of the diver. If a diver quickly rises to the surface, then air dissolved under high pressure begins to be released from the blood in the form of bubbles (just as air dissolved in lemonade, which is in a sealed bottle under high pressure, is released in the form of bubbles when the cork is pulled out). The released blisters cause severe pain throughout the body and can cause serious illness (“caisson disease”). Therefore, a diver who has spent a long time at great depths should be raised to the surface slowly (for hours!) so that the dissolved gases have time to be released gradually, without forming bubbles.
A person's stay under water in an environment that is unusual for him has significant features. When immersed in water, a person, in addition to the atmospheric air pressure that acts on the surface of the water, additionally experiences hydrostatic (excess) pressure. Total (absolute) pressure, measured from zero - complete vacuum, which a person actually experiences under water:
or approximately for fresh water
Pa - where is the absolute water pressure, kgf/cm²;
Pb - atmospheric air pressure, kgf/cm²;
Ri - excess water pressure, kgf/cm²;
B - barometric air pressure, mm Hg. Art.;
Y - specific gravity of water, kgf/m³;
H - immersion depth, m.
Example 1.1. Determine the absolute water pressure acting on a submarine swimmer at a depth of 40 m:
1) at sea, if the atmospheric (barometric) pressure is 760 mm Hg. Art. and the specific gravity of sea water is 1025 kgf/m³;
2) in a mountain lake, if the atmospheric pressure is 600 mm Hg. Art. and the specific gravity of fresh water is 1000 kgf/m³;
3) in a flat reservoir with fresh water, if the atmospheric pressure is 750 mm Hg. Art.
Solution.
Absolute water pressure: 1) in the sea according to (1.1)
2) in a mountain lake according to (1.1)
3) in a flat reservoir according to (1.1)
or according to (1.2)
The results of the example show that in most cases, with sufficient accuracy for practice, approximate formula (1.2) can be used for calculations.
The absolute pressure of water on a person increases significantly with the depth of immersion. So, at a depth of 10 m, compared to atmospheric pressure, it doubles and is equal to 2 kgf/cm² (200 kPa), at a depth of 20 m it triples, etc. However, the relative increase in pressure decreases with increasing depth.
As can be seen from table. 1.1, the greatest relative increase in pressure occurs in the zone of the first ten meters of immersion. In this critical zone, significant physiological overloads are observed, which should not be forgotten, especially for novice underwater swimmers (see 10.2).
Circulation under water, due to uneven hydrostatic pressure on different parts of the body, it has its own characteristics. For example, with a vertical position of a person of average height (170 cm) in water, regardless of the depth of immersion, his feet will experience hydrostatic pressure 0.17 kgf/cm² (17 kPa) more than his head.
Table 1.1. Change in water pressure depending on immersion depth
To the upper areas of the body, where the pressure is less, blood flows in (plethora), from the lower areas of the body, where the pressure is greater, it flows out (partial bleeding). This redistribution of blood flow somewhat increases the load on the heart, which has to overcome greater resistance to the movement of blood through the vessels.
When the body is in a horizontal position in water, the difference in hydrostatic pressure on the chest and back is small - only 0.02...0.03 kgf/cm² (2...3 kPa) and the load on the heart increases slightly.
Breath under water is possible if the external water pressure is equal to the internal air pressure in the “lungs - breathing apparatus” system (Fig. 1.1). Failure to comply with this equality makes breathing difficult or even impossible. Thus, breathing through a tube at a depth of 1 m with a difference between external and internal pressure of 0.1 kgf/cm² (10 kPa) requires a lot of tension in the respiratory muscles and cannot last long, and at a depth of 2 m the respiratory muscles are no longer able to overcome the pressure water on the chest.
A person at rest on the surface takes 12...24 breaths per minute, and his pulmonary ventilation (minute breathing volume) is 6...12 l/min.
Rice. 1.1. Graph of the required air pressure in the “lungs - breathing apparatus” system depending on the depth of immersion: 1 - excess (according to the pressure gauge) air pressure; 2 - absolute air pressure
Under normal conditions, with each inhalation and exhalation, no more than 1/6 of the total air in them is exchanged in the lungs. The rest of the air remains in the alveoli of the lungs and is the medium where gas exchange with the blood occurs. Alveolar air has a constant composition and, unlike atmospheric air, contains 14% oxygen, 5.6% carbon dioxide and 6.2% water vapor (see 1.2).
Even minor changes in its composition lead to physiological changes, which are the body’s compensatory defense. With significant changes, the compensatory defense will not cope, resulting in painful (pathological) conditions (see 10.5...10.8).
Not all air entering the body reaches the pulmonary alveoli, where gas exchange occurs between the blood and lungs. Some of the air fills the body's respiratory tract (trachea, bronchi) and does not participate in the gas exchange process. When you exhale, this air is removed without reaching the alveoli. When you inhale, the alveoli first receive the air that remains in the respiratory tract after exhalation (depleted in oxygen, with a high content of carbon dioxide and water vapor), and then fresh air.
The volume of the body's respiratory tract, in which the air is moistened and warmed but does not participate in gas exchange, is approximately 175 cm³. When swimming with a breathing apparatus (breathing tube), the total volume of the respiratory tract (body and apparatus) almost doubles. At the same time, ventilation of the alveoli worsens and performance decreases.
Intense muscular movements under water require a large consumption of oxygen, which leads to increased pulmonary ventilation, resulting in an increase in the speed of air flow in the respiratory tract of the body and the apparatus (breathing tube). In this case, breathing resistance increases in proportion to the square of the air flow speed. As the density of compressed air increases according to the depth of immersion, breathing resistance also increases.
Breathing resistance has a significant impact on the duration and speed of swimming underwater.
If breathing resistance reaches 60...65 mm Hg. Art. (8...9 kPa), breathing becomes difficult and the respiratory muscles quickly tire. By stretching the inhalation and exhalation phases over time, you can reduce the speed of air flow in the respiratory tract. This leads to a slight decrease in pulmonary ventilation, but at the same time noticeably reduces breathing resistance.
Buoyancy. Due to the high density of water, a person immersed in it is in conditions close to weightlessness. When exhaling, the average specific gravity of a person is in the range of 1020... 1060 kgf/m³ (10.2... 10.6 kN/m³) and negative buoyancy of 1...2 kgf (10...20 N) is observed - the difference between the weight of water displaced by a body and its weight. When inhaling, the average specific gravity of a person decreases to 970 kgf/m³ (9.7 kN/m³) and slight positive buoyancy appears.
When swimming in waterproof clothing, due to the air in its folds, positive buoyancy increases, which makes immersion in water more difficult. Buoyancy can be adjusted using weights. For swimming underwater, a slight negative buoyancy is usually created - 0.5... 1 kgf (5... 10 N). Large negative buoyancy requires constant active movements to maintain at the desired depth and is usually created only when working with support on the ground (object).
Orientation underwater presents certain difficulties. On the surface, a person orients himself in the environment with the help of vision, and his body balance is maintained with the help of the vestibular apparatus, muscular-articular sense and sensations that arise in the internal organs and skin when the body position changes. He constantly experiences the action of gravity (a sense of support) and perceives the slightest change in the position of the body in space.
When swimming underwater, a person is deprived of the usual support. Under these conditions, the only sensory organ that orients a person in space is the vestibular apparatus, the otoliths of which continue to be affected by the forces of gravity. Orientation underwater is especially difficult for a person with zero buoyancy. Underwater, a swimmer with his eyes closed makes errors in determining the position of his body in space at an angle of 10...25°.
The position of a person is of great importance for orientation under water. The most unfavorable position is considered to be on your back with your head thrown back.
When cold water enters the ear canal due to irritation of the vestibular apparatus, the swimmer becomes dizzy, it becomes difficult to determine the direction, and the error often reaches 180°.
To navigate underwater, a swimmer is forced to use external factors that signal the position of the body in space: the movement of bubbles of exhaled air from the apparatus, buoys, etc. A swimmer’s training is of great importance for orientation underwater.
Water resistance has a noticeable effect on swimming speed. When swimming on the surface at a speed of 0.8... 1.7 m/s, the resistance to body movement increases accordingly from 2.5 to 11.5 kgf (from 25 to 115 N). When swimming underwater, there is less resistance to movement, since the underwater swimmer occupies a more horizontal position and does not need to periodically raise his head out of the water to take a breath. In addition, underwater there is less braking force from waves and turbulence resulting from the swimmer’s movements. Experience in the pool shows that the same person who swims a distance of 50 m breaststroke in 37.1 s swims the same distance underwater in 32.2 s.
The average speed of swimming underwater in wetsuits with the apparatus is 0.3...0.5 m/s. At short distances, well-trained swimmers can reach speeds of 0.7.., 1 m/s, well-trained ones - up to 1.5 m/s.
Cooling the body occurs more intensely in water than in air. The thermal conductivity of water is 25 times, and the heat capacity is 4 times greater than air. If a person can be in the air at 4° C for 6 hours without danger to his health and his body temperature does not drop, then in water at the same temperature an unhardened person without protective clothing in most cases dies from hypothermia after 30 ...60 min. Cooling of the body increases with decreasing water temperature and in the presence of current.
In the air environment, intense heat loss at an air temperature of 15...20° C occurs as a result of radiation (40...45%) and evaporation (20...25%), and the share of heat transfer through conduction accounts for only 30.. .35%.
In water, a person without protective clothing loses heat mainly through conduction. In air, heat loss occurs from an area of about 75% of the body surface, since there is heat exchange between the contacting surfaces of the legs, arms and the corresponding areas of the body. In water, heat loss occurs from the entire surface of the body.
Air in direct contact with the skin heats up quickly and is actually at a higher temperature than the surrounding air. Even the wind cannot completely remove this layer of warm air from the skin. In water, with its high specific heat capacity and high thermal conductivity, the layer adjacent to the body does not have time to heat up and is easily displaced by cold water. Therefore, the body surface temperature in water decreases more intensely than in air. In addition, due to uneven hydrostatic pressure of water, the lower areas of the body, which experience greater pressure, are cooled more and have a lower skin temperature than the upper areas, which are less compressed by water.
The body's thermal sensations in air and in water at the same temperature are different. In table 1.2 provides a comparative description of human sensations at the same temperature of water and air.
Table 1.2. Thermal sensations of the body in air and water
Due to intense cooling and compression by hydrostatic pressure, skin sensitivity in water is reduced, pain is dulled, so small cuts and even wounds may go unnoticed.
When going underwater in waterproof clothing, the skin temperature decreases unevenly. The greatest drop in skin temperature is observed in the extremities (Table 1.3).
Audibility in water worsens, since sounds under water are perceived mainly through bone conduction, which is 40% lower than air conduction.
The range of audibility during bone conduction depends on the pitch of the sound: the higher the tone, the better the sound is heard. This is of practical importance for the connection of swimmers with each other and with the surface.
When diving in equipment with a voluminous helmet, air conduction is maintained almost completely.
Table 1.3. Average skin temperature of a submarine swimmer after staying in cold water (1...9°C) in hydroprotective clothing for 2 hours
Sound in water travels 4.5 times faster than in the atmosphere, so under water a signal from a sound source located on the side arrives at both ears almost simultaneously, the difference being less than 0.00-001 s. Such a slight difference in the time of signal arrival is not differentiated well enough, and a clear spatial perception of sound does not occur. Consequently, it is difficult for a person to establish the direction of the sound source under water.
Visibility in water depends on the quantity and composition of substances dissolved in it, suspended particles that scatter light rays. In muddy water, even in clear sunny weather, visibility is almost non-existent.
The depth of light penetration into the water column depends on the angle of incidence of the rays and the state of the water surface. Oblique solar rays falling on the surface of the water penetrate to a shallow depth, and most of them are reflected from the surface of the water. Faint ripples or waves dramatically reduce visibility in the water.
At a depth of 10 m, illumination is 4 times less than on the surface. At a depth of 20 m, illumination decreases by 8 times, and at a depth of 50 m - by several tens of times. Rays of different wavelengths are absorbed unevenly. The long-wavelength part of the visible spectrum (red rays) is almost completely absorbed by the surface layers of water. The short-wave part (violet rays) in the most transparent ocean water can penetrate to a depth of no more than 1000... 1500 m. Green rays do not penetrate deeper than 100 m.
Underwater vision has its own characteristics. Water has approximately the same refractive power as the optical system of the eye. If a swimmer dives without a mask, light rays pass through the water and enter the eye without being refracted. In this case, the rays converge not at the retina, but much further, behind it. As a result, visual acuity deteriorates 100...200 times, and the field of vision decreases, the image of objects turns out to be unclear, blurry, and the person becomes farsighted.
When a diver wearing a mask dives, a light ray from the water passes through the layer of air in the mask, enters the eye and is refracted in its optical system as usual. But the underwater swimmer sees the image of the object somewhat closer and higher than its actual location. The objects themselves seem much larger under water than in reality. Experienced swimmers adapt to these visual features and do not experience any difficulties.
Color perception also deteriorates sharply in water. Blue and green colors, which are close to the natural color of water, are especially poorly perceived; white and orange are best.
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