Let us examine in more detail the experiment with a piston sucking water in a tube. At the beginning of the experiment (Fig. 287), the water in the tube and in the cup is at the same level and the piston touches the water with its lower surface. The water is pressed against the piston from below by atmospheric pressure acting on the surface of the water in the cup. On top of the piston (we will consider it weightless) also acts atmospheric pressure. For its part, the piston, according to the law of equality of action and reaction, acts on the water in the tube, exerting on it a pressure equal to the atmospheric pressure acting on the surface of the water in the cup.
Rice. 287. Suction of water into a tube. Beginning of the experiment: the piston is at the level of water in the cup
Rice. 288. a) The same as in Fig. 287, but with the piston raised, b) Pressure graph
Let us now raise the piston to a certain height; to do this, a force directed upward will have to be applied to it (Fig. 288, a). Atmospheric pressure will force water into the tube following the piston; Now the column of water will touch the piston, pressing against it with less force, that is, exert less pressure on it than before. Accordingly, the counterpressure of the piston on the water in the tube will be less. The atmospheric pressure acting on the surface of the water in the cup will be balanced by the pressure of the piston added to the pressure created by the water column in the tube.
In Fig. 288, b shows a graph of pressure in a rising column of water in a tube. If we raise the piston to a greater height, the water will also rise, following the piston, and the water column will become higher. The pressure caused by the weight of the pillar will increase; consequently, the pressure of the piston on the upper end of the column will decrease, since both of these pressures must still add up to atmospheric pressure. Now the water will be pressed against the piston with even less force. To hold the piston in place, you will now have to apply more force: as the piston is raised, the water pressure on the lower surface of the piston will balance out the atmospheric pressure on its upper surface to a lesser extent.
What happens if, taking a tube of sufficient length, you raise the piston higher and higher? The water pressure on the piston will become less and less; Finally, the water pressure on the piston and the piston pressure on the water will go to zero. At this height of the column, the pressure caused by the weight of the water in the tube will be equal to atmospheric pressure. The calculation that we will present in the next paragraph shows that the height of the water column should be equal to 10.332 m (at normal atmospheric pressure). With further rise of the piston, the level of the water column will no longer increase, since external pressure is not able to balance the higher column: empty space will remain between the water and the lower surface of the piston (Fig. 289, a).
Rice. 289. a) The same as in Fig. 288, but when the piston is raised higher maximum height(10.33 m). b) Pressure graph for this piston position. c) In reality, the water column does not reach its full height, since water vapor has a pressure of about 20 mm Hg at room temperature. Art. and accordingly lowers the upper level of the column. Therefore, the true graph has a cut off top. For clarity, water vapor pressure is exaggerated
In reality, this space will not be completely empty: it will be filled with air released from the water, in which there is always some dissolved air; in addition, there will be water vapor in this space. Therefore, the pressure in the space between the piston and the water column will not be exactly zero, and this pressure will slightly reduce the height of the column (Fig. 289, c).
The described experiment is very cumbersome due to the high height of the water column. If this experiment were repeated, replacing water with mercury, the height of the column would be much smaller. However, instead of a tube with a piston, it is much more convenient to use the device described in the next paragraph.
173.1. To what maximum height can a suction pump lift mercury in a tube if the atmospheric pressure is ?
A man with and without skis.
A person walks through loose snow with great difficulty, sinking deeply with every step. But, having put on skis, he can walk without almost falling into it. Why? With or without skis, a person acts on the snow with the same force equal to his weight. However, the effect of this force is different in both cases, because the surface area on which a person presses is different, with skis and without skis. Almost 20 times the surface area of skis more area soles. Therefore, when standing on skis, a person acts on every square centimeter of the snow surface with a force that is 20 times less than when standing on the snow without skis.
A student, pinning a newspaper to the board with buttons, acts on each button with equal force. However, a button with a sharper end will go into the wood more easily.
This means that the result of the force depends not only on its modulus, direction and point of application, but also on the area of the surface to which it is applied (perpendicular to which it acts).
This conclusion is confirmed by physical experiments.
Experience. The result of the action of a given force depends on what force acts on a unit surface area.
You need to drive nails into the corners of a small board. First, place the nails driven into the board on the sand with their points up and place a weight on the board. In this case, the nail heads are only slightly pressed into the sand. Then we turn the board over and place the nails on the edge. In this case, the support area is smaller, and under the same force the nails go significantly deeper into the sand.
Experience. Second illustration.
The result of the action of this force depends on what force acts on each unit of surface area.
In the examples considered, the forces acted perpendicular to the surface of the body. The man's weight was perpendicular to the surface of the snow; the force acting on the button is perpendicular to the surface of the board.
The quantity equal to the ratio of the force acting perpendicular to the surface to the area of this surface is called pressure.
To determine the pressure, the force acting perpendicular to the surface must be divided by the surface area:
pressure = force / area.
Let us denote the quantities included in this expression: pressure - p, the force acting on the surface is F and surface area - S.
Then we get the formula:
p = F/S
It is clear that a larger force acting on the same area will produce greater pressure.
The unit of pressure is taken to be the pressure produced by a force of 1 N acting on a surface with an area of 1 m2 perpendicular to this surface.
Unit of pressure - newton per square meter (1 N/m2). In honor of the French scientist Blaise Pascal it's called pascal ( Pa). Thus,
1 Pa = 1 N/m2.
Other units of pressure are also used: hectopascal (hPa) And kilopascal (kPa).
1 kPa = 1000 Pa;
1 hPa = 100 Pa;
1 Pa = 0.001 kPa;
1 Pa = 0.01 hPa.
Let's write down the conditions of the problem and solve it.
Given : m = 45 kg, S = 300 cm 2; p = ?
In SI units: S = 0.03 m2
Solution:
p = F/S,
F = P,
P = g m,
P= 9.8 N · 45 kg ≈ 450 N,
p= 450/0.03 N/m2 = 15000 Pa = 15 kPa
"Answer": p = 15000 Pa = 15 kPa
Ways to reduce and increase pressure.
A heavy crawler tractor produces a pressure on the soil equal to 40 - 50 kPa, i.e. only 2 - 3 times more than the pressure of a boy weighing 45 kg. This is explained by the fact that the weight of the tractor is distributed over a larger area due to the track drive. And we have established that the larger the support area, the less pressure produced by the same force on this support .
Depending on whether you need to get small or high pressure, the support area increases or decreases. For example, in order for the soil to withstand the pressure of the building being erected, the area of the lower part of the foundation is increased.
Tires trucks and the landing gear of aircraft is made much wider than that of passenger cars. The tires of cars designed for driving in deserts are made especially wide.
Heavy vehicles, such as a tractor, a tank or a swamp vehicle, having a large support area of the tracks, pass through swampy areas that cannot be passed by a person.
On the other hand, with a small surface area, a large amount of pressure can be generated with a small force. For example, when pressing a button into a board, we act on it with a force of about 50 N. Since the area of the tip of the button is approximately 1 mm 2, the pressure produced by it is equal to:
p = 50 N / 0.000 001 m 2 = 50,000,000 Pa = 50,000 kPa.
For comparison, this pressure is 1000 times greater than the pressure exerted by a crawler tractor on the soil. You can find many more such examples.
The blades of cutting instruments and the points of piercing instruments (knives, scissors, cutters, saws, needles, etc.) are specially sharpened. The sharpened edge of a sharp blade has a small area, so even a small force creates a lot of pressure, and this tool is easy to work with.
Cutting and piercing devices are also found in living nature: these are teeth, claws, beaks, spikes, etc. - they are all made of hard material, smooth and very sharp.
Pressure
It is known that gas molecules move randomly.
We already know that gases, unlike solids and liquids, fill the entire container in which they are located. For example, steel gas storage cylinder, chamber car tire or a volleyball. In this case, the gas exerts pressure on the walls, bottom and lid of the cylinder, chamber or any other body in which it is located. Gas pressure is caused by factors other than pressure solid on the support.
It is known that gas molecules move randomly. As they move, they collide with each other, as well as with the walls of the container containing the gas. There are many molecules in a gas, and therefore the number of their impacts is very large. For example, the number of impacts of air molecules in a room on a surface with an area of \u200b\u200b1 cm 2 in 1 s is expressed as a twenty-three-digit number. Although the impact force of an individual molecule is small, the effect of all molecules on the walls of the vessel is significant - it creates gas pressure.
So, gas pressure on the walls of the container (and on the body placed in the gas) is caused by impacts of gas molecules .
Let's consider next experience. Under the bell air pump place a rubber ball. It contains a small amount of air and has irregular shape. Then we pump out the air from under the bell. The shell of the ball, around which the air becomes increasingly rarefied, gradually inflates and takes the shape of a regular ball.
How to explain this experience?
Special durable steel cylinders are used for storing and transporting compressed gas.
In our experiment, moving gas molecules continuously hit the walls of the ball inside and outside. When air is pumped out, the number of molecules in the bell around the shell of the ball decreases. But inside the ball their number does not change. Therefore, the number of impacts of molecules on the outer walls of the shell becomes less than the number of impacts on the inner walls. The ball inflates until the elastic force of its rubber shell becomes equal to the force of gas pressure. The shell of the ball takes the shape of a ball. This shows that the gas presses on its walls equally in all directions. In other words, the number of molecular impacts per square centimeter of surface area is the same in all directions. The same pressure in all directions is characteristic of a gas and is a consequence of the random movement of a huge number of molecules.
Let's try to reduce the volume of gas, but so that its mass remains unchanged. This means that in every cubic centimeter of gas there will be more molecules, and the density of the gas will increase. Then the number of impacts of molecules on the walls will increase, i.e., the gas pressure will increase. This can be confirmed by experience.
In the picture A shows a glass tube, one end of which is closed with a thin rubber film. A piston is inserted into the tube. When the piston moves in, the volume of air in the tube decreases, i.e. the gas is compressed. The rubber film bends outward, indicating that the air pressure in the tube has increased.
On the contrary, as the volume of the same mass of gas increases, the number of molecules in each cubic centimeter decreases. This will reduce the number of impacts on the walls of the vessel - the gas pressure will become less. Indeed, when the piston is pulled out of the tube, the volume of air increases and the film bends inside the vessel. This indicates a decrease in air pressure in the tube. The same phenomena would be observed if instead of air there was any other gas in the tube.
So, when the volume of a gas decreases, its pressure increases, and when the volume increases, the pressure decreases, provided that the mass and temperature of the gas remain unchanged.
How will the pressure of a gas change if it is heated at a constant volume? It is known that the speed of gas molecules increases when heated. Moving faster, the molecules will hit the walls of the container more often. In addition, each impact of the molecule on the wall will be stronger. As a result, the walls of the vessel will experience greater pressure.
Hence, The higher the gas temperature, the greater the gas pressure in a closed vessel, provided that the gas mass and volume do not change.
From these experiments it can be generally concluded that The gas pressure increases the more often and harder the molecules hit the walls of the vessel .
To store and transport gases, they are highly compressed. At the same time, their pressure increases, the gases must be enclosed in special, very durable cylinders. Such cylinders, for example, contain compressed air in submarines, oxygen used in metal welding. Of course, we must always remember that gas cylinders cannot be heated, especially when they are filled with gas. Because, as we already understand, an explosion can occur with very unpleasant consequences.
Pascal's law.
Pressure is transmitted to every point in the liquid or gas.
The pressure of the piston is transmitted to each point of the fluid filling the ball.
Now gas.
Unlike solids, individual layers and fine particles liquids and gases can move freely relative to each other in all directions. It is enough, for example, to lightly blow on the surface of the water in a glass to cause the water to move. On a river or lake, the slightest breeze causes ripples to appear.
The mobility of gas and liquid particles explains that the pressure exerted on them is transmitted not only in the direction of the force, but to every point. Let's consider this phenomenon in more detail.
In the picture, A depicts a vessel containing gas (or liquid). The particles are evenly distributed throughout the vessel. The vessel is closed by a piston that can move up and down.
By applying some force, we will force the piston to move slightly inward and compress the gas (liquid) located directly below it. Then the particles (molecules) will be located in this place more densely than before (Fig, b). Due to mobility, gas particles will move in all directions. As a result, their arrangement will again become uniform, but more dense than before (Fig. c). Therefore, gas pressure will increase everywhere. This means that additional pressure is transmitted to all particles of gas or liquid. So, if the pressure on the gas (liquid) near the piston itself increases by 1 Pa, then at all points inside gas or liquid, the pressure will become greater than before by the same amount. The pressure on the walls of the vessel, the bottom, and the piston will increase by 1 Pa.
The pressure exerted on a liquid or gas is transmitted to any point equally in all directions .
This statement is called Pascal's law.
Based on Pascal's law, it is easy to explain the following experiments.
The picture shows a hollow ball with small holes in various places. A tube is attached to the ball into which a piston is inserted. If you fill a ball with water and push a piston into the tube, water will flow out of all the holes in the ball. In this experiment, a piston presses on the surface of water in a tube. The water particles located under the piston, condensing, transfer its pressure to other layers that lie deeper. Thus, the pressure of the piston is transmitted to each point of the fluid filling the ball. As a result, part of the water is pushed out of the ball in the form of identical streams flowing from all holes.
If the ball is filled with smoke, then when the piston is pushed into the tube, equal streams of smoke will begin to come out of all the holes in the ball. This confirms that gases transmit the pressure exerted on them in all directions equally.
Pressure in liquid and gas.
Under the influence of the weight of the liquid, the rubber bottom in the tube will bend.
Liquids, like all bodies on Earth, are affected by gravity. Therefore, each layer of liquid poured into a vessel creates pressure with its weight, which, according to Pascal’s law, is transmitted in all directions. Therefore, there is pressure inside the liquid. This can be verified by experience.
Pour water into a glass tube, the bottom hole of which is closed with a thin rubber film. Under the influence of the weight of the liquid, the bottom of the tube will bend.
Experience shows that the higher the column of water above the rubber film, the more it bends. But every time after the rubber bottom bends, the water in the tube comes to equilibrium (stops), since, in addition to the force of gravity, the elastic force of the stretched rubber film acts on the water.
The forces acting on the rubber film are |
are the same on both sides. |
Illustration.
The bottom moves away from the cylinder due to the pressure of gravity on it.
Let's lower the tube with a rubber bottom, into which water is poured, into another, wider vessel with water. We will see that as the tube is lowered, the rubber film gradually straightens. Full straightening of the film shows that the forces acting on it from above and below are equal. Complete straightening of the film occurs when the water levels in the tube and vessel coincide.
The same experiment can be carried out with a tube in which a rubber film covers the side hole, as shown in figure a. Let's immerse this tube with water in another vessel with water, as shown in the figure, b. We will notice that the film will straighten again as soon as the water levels in the tube and the vessel are equal. This means that the forces acting on the rubber film are the same on all sides.
Let's take a vessel whose bottom can fall away. Let's put it in a jar of water. The bottom will be tightly pressed to the edge of the vessel and will not fall off. It is pressed by the force of water pressure directed from bottom to top.
We will carefully pour water into the vessel and watch its bottom. As soon as the water level in the vessel coincides with the water level in the jar, it will fall away from the vessel.
At the moment of separation, a column of liquid in the vessel presses from top to bottom, and pressure from a column of liquid of the same height, but located in the jar, is transmitted from bottom to top to the bottom. Both of these pressures are the same, but the bottom moves away from the cylinder due to the action on it own strength gravity.
Experiments with water were described above, but if you take any other liquid instead of water, the results of the experiment will be the same.
So, experiments show that There is pressure inside the liquid, and at the same level it is equal in all directions. Pressure increases with depth.
Gases are no different from liquids in this respect, because they also have weight. But we must remember that the density of gas is hundreds of times less than the density of liquid. The weight of the gas in the vessel is small, and its “weight” pressure in many cases can be ignored.
Calculation of liquid pressure on the bottom and walls of a vessel.
Calculation of liquid pressure on the bottom and walls of a vessel.
Let's consider how you can calculate the pressure of a liquid on the bottom and walls of a vessel. Let us first solve the problem for a vessel shaped like a rectangular parallelepiped.
Strength F, with which the liquid poured into this vessel presses on its bottom, is equal to the weight P liquid in the container. The weight of a liquid can be determined by knowing its mass m. Mass, as you know, can be calculated using the formula: m = ρ·V. The volume of liquid poured into the vessel we have chosen is easy to calculate. If the height of the liquid column in a vessel is denoted by the letter h, and the area of the bottom of the vessel S, That V = S h.
Liquid mass m = ρ·V, or m = ρ S h .
The weight of this liquid P = g m, or P = g ρ S h.
Since the weight of a column of liquid is equal to the force with which the liquid presses on the bottom of the vessel, then by dividing the weight P per area S, we get the fluid pressure p:
p = P/S, or p = g·ρ·S·h/S,
We have obtained a formula for calculating the pressure of the liquid at the bottom of the vessel. From this formula it is clear that the pressure of the liquid at the bottom of the vessel depends only on the density and height of the liquid column.
Therefore, using the formula derived, you can calculate the pressure of the liquid poured into the vessel any shape(strictly speaking, our calculation is only suitable for vessels having the shape of a straight prism and a cylinder. In physics courses for the institute, it was proven that the formula is also true for a vessel of arbitrary shape). In addition, it can be used to calculate the pressure on the walls of the vessel. The pressure inside the liquid, including the pressure from bottom to top, is also calculated using this formula, since the pressure at the same depth is the same in all directions.
When calculating pressure using the formula p = gρh you need density ρ express in kilograms per cubic meter(kg/m 3), and the height of the liquid column h- in meters (m), g= 9.8 N/kg, then the pressure will be expressed in pascals (Pa).
Example. Determine the oil pressure at the bottom of the tank if the height of the oil column is 10 m and its density is 800 kg/m3.
Let's write down the condition of the problem and write it down.
Given :
ρ = 800 kg/m 3
Solution :
p = 9.8 N/kg · 800 kg/m 3 · 10 m ≈ 80,000 Pa ≈ 80 kPa.
Answer : p ≈ 80 kPa.
Communicating vessels.
Communicating vessels.
The figure shows two vessels connected to each other by a rubber tube. Such vessels are called communicating. A watering can, a teapot, a coffee pot are examples of communicating vessels. From experience we know that water poured, for example, into a watering can is always at the same level in the spout and inside.
We often encounter communicating vessels. For example, it could be a teapot, watering can or coffee pot. |
The surfaces of a homogeneous liquid are installed at the same level in communicating vessels of any shape. |
Liquids of different densities. |
The following simple experiment can be done with communicating vessels. At the beginning of the experiment, we clamp the rubber tube in the middle and pour water into one of the tubes. Then we open the clamp, and the water instantly flows into the other tube until the water surfaces in both tubes are at the same level. You can mount one of the handsets on a tripod and raise, lower, or tilt the other different sides. And in this case, as soon as the liquid calms down, its levels in both tubes will be equalized.
In communicating vessels of any shape and cross-section, the surfaces of a homogeneous liquid are set at the same level(provided that the air pressure above the liquid is the same) (Fig. 109).
This can be justified as follows. The liquid is at rest without moving from one vessel to another. This means that the pressure in both vessels at any level is the same. The liquid in both vessels is the same, i.e. it has the same density. Therefore, its heights must be the same. When we lift one container or add liquid to it, the pressure in it increases and the liquid moves into another container until the pressures are balanced.
If a liquid of one density is poured into one of the communicating vessels, and a liquid of another density is poured into the second, then at equilibrium the levels of these liquids will not be the same. And this is understandable. We know that the pressure of the liquid at the bottom of the vessel is directly proportional to the height of the column and the density of the liquid. And in this case, the densities of the liquids will be different.
If the pressures are equal, the height of a column of liquid with a higher density will be less than the height of a column of liquid with a lower density (Fig.).
Experience. How to determine the mass of air.
Air weight. Atmospheric pressure.
The existence of atmospheric pressure.
Atmospheric pressure is greater than the pressure of rarefied air in the vessel.
Air, like any body on Earth, is affected by gravity, and therefore air has weight. The weight of air is easy to calculate if you know its mass.
We will show you experimentally how to calculate the mass of air. To do this, you need to take a durable glass ball with a stopper and a rubber tube with a clamp. Let's pump the air out of it, clamp the tube with a clamp and balance it on the scales. Then, opening the clamp on the rubber tube, let air into it. This will upset the balance of the scales. To restore it, you will have to put weights on the other pan of the scale, the mass of which will be equal to the mass of air in the volume of the ball.
Experiments have established that at a temperature of 0 °C and normal atmospheric pressure, the mass of air with a volume of 1 m 3 is equal to 1.29 kg. The weight of this air is easy to calculate:
P = g m, P = 9.8 N/kg 1.29 kg ≈ 13 N.
air shell, surrounding the Earth, called atmosphere (from Greek atmos- steam, air, and sphere- ball).
The atmosphere, as shown by observations of the flight of artificial Earth satellites, extends to an altitude of several thousand kilometers.
Due to gravity, the upper layers of the atmosphere, like ocean water, compress the lower layers. The air layer adjacent directly to the Earth is compressed the most and, according to Pascal's law, transmits the pressure exerted on it in all directions.
As a result of this, the earth's surface and the bodies located on it experience pressure from the entire thickness of the air, or, as is usually said in such cases, experience atmospheric pressure .
The existence of atmospheric pressure can explain many phenomena that we encounter in life. Let's look at some of them.
The figure shows a glass tube, inside of which there is a piston that fits tightly to the walls of the tube. The end of the tube is lowered into water. If you lift the piston, the water will rise behind it.
This phenomenon is used in water pumps and some other devices.
The figure shows a cylindrical vessel. It is closed with a stopper into which a tube with a tap is inserted. Air is pumped out of the vessel using a pump. The end of the tube is then placed in water. If you now open the tap, water will spray like a fountain into the inside of the vessel. Water enters the vessel because atmospheric pressure is greater than the pressure of rarefied air in the vessel.
Why does the Earth's air envelope exist?
Like all bodies, the gas molecules that make up the Earth's air envelope are attracted to the Earth.
But why then don’t they all fall to the surface of the Earth? How is the Earth's air envelope and its atmosphere preserved? To understand this, we must take into account that gas molecules are in continuous and random motion. But then another question arises: why don’t these molecules fly away into outer space, that is, into space.
In order to completely leave the Earth, a molecule, like spacecraft or a rocket, must have a very high speed (not less than 11.2 km/s). This is the so-called second escape velocity. The speed of most molecules in the Earth's air shell is significantly less than this escape velocity. Therefore, most of them are tied to the Earth by gravity, only a negligible number of molecules fly beyond the Earth into space.
The random movement of molecules and the effect of gravity on them result in gas molecules “hovering” in space near the Earth, forming an air envelope, or the atmosphere known to us.
Measurements show that air density decreases rapidly with altitude. So, at an altitude of 5.5 km above the Earth, the density of air is 2 times less than its density at the surface of the Earth, at an altitude of 11 km - 4 times less, etc. The higher it is, the rarer the air. And finally, in the most upper layers(hundreds and thousands of kilometers above the Earth) the atmosphere gradually turns into airless space. The Earth's air envelope does not have a clear boundary.
Strictly speaking, due to the action of gravity, the gas density in any closed vessel is not the same throughout the entire volume of the vessel. At the bottom of the vessel, the gas density is greater than in its upper parts, therefore the pressure in the vessel is not the same. It is larger at the bottom of the vessel than at the top. However, for a gas contained in a vessel, this difference in density and pressure is so small that in many cases it can be completely ignored, just known about it. But for an atmosphere extending over several thousand kilometers, this difference is significant.
Measuring atmospheric pressure. Torricelli's experience.
It is impossible to calculate atmospheric pressure using the formula for calculating the pressure of a liquid column (§ 38). For such a calculation, you need to know the height of the atmosphere and air density. But the atmosphere does not have a definite boundary, and the density of air at different altitudes is different. However, atmospheric pressure can be measured using an experiment proposed in the 17th century by an Italian scientist Evangelista Torricelli , student of Galileo.
Torricelli's experiment consists of the following: a glass tube about 1 m long, sealed at one end, is filled with mercury. Then, tightly closing the second end of the tube, it is turned over and lowered into a cup of mercury, where this end of the tube is opened under the level of mercury. As in any experiment with liquid, part of the mercury is poured into the cup, and part of it remains in the tube. The height of the column of mercury remaining in the tube is approximately 760 mm. There is no air above the mercury inside the tube, there is an airless space, so no gas exerts pressure from above on the column of mercury inside this tube and does not affect the measurements.
Torricelli, who proposed the experiment described above, also gave its explanation. The atmosphere presses on the surface of the mercury in the cup. Mercury is in equilibrium. This means that the pressure in the tube is at the level ahh 1 (see figure) is equal to atmospheric pressure. When atmospheric pressure changes, the height of the mercury column in the tube also changes. As pressure increases, the column lengthens. As the pressure decreases, the mercury column decreases its height.
The pressure in the tube at level aa1 is created by the weight of the mercury column in the tube, since there is no air above the mercury in the upper part of the tube. It follows that atmospheric pressure is equal to the pressure of the mercury column in the tube , i.e.
p atm = p mercury
The higher the atmospheric pressure, the higher the mercury column in Torricelli's experiment. Therefore, in practice, atmospheric pressure can be measured by the height of the mercury column (in millimeters or centimeters). If, for example, the atmospheric pressure is 780 mm Hg. Art. (they say “millimeters of mercury”), this means that the air produces the same pressure as a vertical column of mercury 780 mm high.
Therefore, in this case, the unit of measurement for atmospheric pressure is 1 millimeter of mercury (1 mm Hg). Let's find the relationship between this unit and the unit known to us - pascal(Pa).
The pressure of a mercury column ρ of mercury with a height of 1 mm is equal to:
p = g·ρ·h, p= 9.8 N/kg · 13,600 kg/m 3 · 0.001 m ≈ 133.3 Pa.
So, 1 mmHg. Art. = 133.3 Pa.
Currently, atmospheric pressure is usually measured in hectopascals (1 hPa = 100 Pa). For example, weather reports may announce that the pressure is 1013 hPa, which is the same as 760 mmHg. Art.
Observing the height of the mercury column in the tube every day, Torricelli discovered that this height changes, that is, atmospheric pressure is not constant, it can increase and decrease. Torricelli also noted that atmospheric pressure is associated with changes in weather.
If you attach a vertical scale to the tube of mercury used in Torricelli’s experiment, you get the simplest device - mercury barometer (from Greek baros- heaviness, metreo- I measure). It is used to measure atmospheric pressure.
Barometer - aneroid.
In practice, a metal barometer called a barometer is used to measure atmospheric pressure. aneroid (translated from Greek - aneroid). This is what a barometer is called because it contains no mercury.
The appearance of the aneroid is shown in the figure. Its main part is a metal box 1 with a wavy (corrugated) surface (see other figure). The air is pumped out of this box, and to prevent atmospheric pressure from crushing the box, its lid 2 is pulled upward by a spring. As atmospheric pressure increases, the lid bends down and tightens the spring. As the pressure decreases, the spring straightens the cap. An indicator arrow 4 is attached to the spring using a transmission mechanism 3, which moves to the right or left when the pressure changes. Under the arrow there is a scale, the divisions of which are marked according to the readings of the mercury barometer. Thus, the number 750, against which the aneroid arrow stands (see figure), shows that in at the moment in a mercury barometer, the height of the mercury column is 750 mm.
Therefore, the atmospheric pressure is 750 mmHg. Art. or ≈ 1000 hPa.
The value of atmospheric pressure is very important for predicting the weather for the coming days, since changes in atmospheric pressure are associated with changes in weather. A barometer is a necessary instrument for meteorological observations.
Atmospheric pressure at different altitudes.
In a liquid, pressure, as we know, depends on the density of the liquid and the height of its column. Due to low compressibility, the density of the liquid at different depths is almost the same. Therefore, when calculating pressure, we consider its density constant and take into account only the change in height.
The situation with gases is more complicated. Gases are highly compressible. And the more a gas is compressed, the greater its density, and the greater the pressure it produces. After all, gas pressure is created by the impacts of its molecules on the surface of the body.
The layers of air near the Earth's surface are compressed by all the overlying layers of air above them. But the higher the layer of air is from the surface, the weaker it is compressed, the lower its density. Therefore, the less pressure it produces. If, for example, balloon rises above the Earth's surface, the air pressure on the ball becomes less. This happens not only because the height of the air column above it decreases, but also because the density of the air decreases. It is smaller at the top than at the bottom. Therefore, the dependence of air pressure on altitude is more complex than that of liquids.
Observations show that atmospheric pressure in areas at sea level is on average 760 mm Hg. Art.
Atmospheric pressure equal to the pressure of a column of mercury 760 mm high at a temperature of 0 ° C is called normal atmospheric pressure.
Normal atmospheric pressure equals 101,300 Pa = 1013 hPa.
How more height above sea level, the lower the pressure.
With small climbs, on average, for every 12 m of rise, the pressure decreases by 1 mmHg. Art. (or by 1.33 hPa).
Knowing the dependence of pressure on altitude, one can determine the altitude above sea level by changes in barometer readings. Aneroids that have a scale by which height above sea level can be directly measured are called altimeters . They are used in aviation and mountain climbing.
Pressure gauges.
We already know that barometers are used to measure atmospheric pressure. To measure pressures greater or less than atmospheric pressure, it is used pressure gauges (from Greek manos- rare, loose, metreo- I measure). There are pressure gauges liquid And metal.
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Let's first consider the device and action open liquid pressure gauge . It consists of a two-legged glass tube into which some liquid is poured. The liquid is installed in both elbows at the same level, since only atmospheric pressure acts on its surface in the vessel elbows.
To understand how such a pressure gauge works, it can be connected by a rubber tube to a round flat box, one side of which is covered with rubber film. If you press your finger on the film, the liquid level in the pressure gauge elbow connected to the box will decrease, and in the other elbow it will increase. What explains this?
When pressing on the film, the air pressure in the box increases. According to Pascal's law, this increase in pressure is also transmitted to the fluid in the pressure gauge elbow that is connected to the box. Therefore, the pressure on the fluid in this elbow will be greater than in the other, where only atmospheric pressure acts on the fluid. Under the force of this excess pressure, the liquid will begin to move. In the elbow with compressed air the liquid will fall, in the other it will rise. The fluid will come to equilibrium (stop) when the excess pressure compressed air will be balanced by the pressure produced by the excess column of liquid in the other leg of the pressure gauge.
The harder you press on the film, the higher the excess liquid column, the greater its pressure. Hence, the change in pressure can be judged by the height of this excess column.
The figure shows how such a pressure gauge can measure the pressure inside a liquid. The deeper the tube is immersed in the liquid, the greater the difference in the heights of the liquid columns in the pressure gauge elbows becomes., therefore, and more pressure is generated by the fluid.
If you install the device box at some depth inside the liquid and turn it with the film up, sideways and down, the pressure gauge readings will not change. That's how it should be, because at the same level inside a liquid, the pressure is equal in all directions.
The picture shows metal pressure gauge . The main part of such a pressure gauge is a metal tube bent into a pipe 1 , one end of which is closed. The other end of the tube using a tap 4 communicates with the vessel in which the pressure is measured. As the pressure increases, the tube unbends. Movement of its closed end using a lever 5 and teeth 3 transmitted to the arrow 2 , moving near the instrument scale. When the pressure decreases, the tube, due to its elasticity, returns to its previous position, and the arrow returns to the zero division of the scale.
Piston liquid pump.
In the experiment we considered earlier (§ 40), it was established that the water in the glass tube, under the influence of atmospheric pressure, rose upward behind the piston. This is what the action is based on. piston pumps
The pump is shown schematically in the figure. It consists of a cylinder, inside of which a piston moves up and down, tightly adjacent to the walls of the vessel. 1 . Valves are installed at the bottom of the cylinder and in the piston itself 2 , opening only upwards. When the piston moves upward, water under the influence of atmospheric pressure enters the pipe, lifts the lower valve and moves behind the piston.
As the piston moves downward, the water under the piston presses on the bottom valve and it closes. At the same time, under water pressure, a valve inside the piston opens, and water flows into the space above the piston. The next time the piston moves upward, the water above it also rises and pours into the outlet pipe. At the same time, a new portion of water rises behind the piston, which, when the piston is subsequently lowered, will appear above it, and this whole procedure is repeated again and again while the pump is running.
Hydraulic press.
Pascal's law explains the action hydraulic machine (from Greek hydraulics- water). These are machines whose operation is based on the laws of motion and equilibrium of fluids.
The main part of the hydraulic machine is two cylinders different diameters, equipped with pistons and a connecting tube. The space under the pistons and the tube are filled with liquid (usually mineral oil). The heights of the liquid columns in both cylinders are the same as long as no forces act on the pistons.
Let us now assume that the forces F 1 and F 2 - forces acting on the pistons, S 1 and S 2 - piston areas. The pressure under the first (small) piston is equal to p 1 = F 1 / S 1, and under the second (large) p 2 = F 2 / S 2. According to Pascal's law, pressure is transmitted equally in all directions by a fluid at rest, i.e. p 1 = p 2 or F 1 / S 1 = F 2 / S 2, from:
F 2 / F 1 = S 2 / S 1 .
Therefore, the strength F 2 so many times more power F 1 , How many times is the area of the large piston greater than the area of the small piston?. For example, if the area of the large piston is 500 cm2, and the small one is 5 cm2, and a force of 100 N acts on the small piston, then a force 100 times greater, that is, 10,000 N, will act on the larger piston.
Thus, with the help of a hydraulic machine, it is possible to balance a larger force with a small force.
Attitude F 1 / F 2 shows the gain in strength. For example, in the example given, the gain in strength is 10,000 N / 100 N = 100.
A hydraulic machine used for pressing (squeezing) is called hydraulic press .
Hydraulic presses are used where greater force is required. For example, for squeezing oil from seeds in oil mills, for pressing plywood, cardboard, hay. In metallurgical plants, hydraulic presses are used to make steel machine shafts, railroad wheels, and many other products. Modern hydraulic presses can develop forces of tens and hundreds of millions of newtons.
Device hydraulic press shown schematically in the figure. The pressed body 1 (A) is placed on a platform connected to the large piston 2 (B). With the help of a small piston 3 (D), high pressure is created on the liquid. This pressure is transmitted to every point of the fluid filling the cylinders. Therefore, the same pressure acts on the second, larger piston. But since the area of the 2nd (large) piston is greater than the area of the small one, the force acting on it will be greater than the force acting on piston 3 (D). Under the influence of this force, piston 2 (B) will rise. When piston 2 (B) rises, body (A) rests against the stationary upper platform and is compressed. Pressure gauge 4 (M) measures the fluid pressure. Safety valve 5 (P) automatically opens when the fluid pressure exceeds the permissible value.
From the small cylinder to the large one, the liquid is pumped by repeated movements of the small piston 3 (D). This is done as follows. When the small piston (D) rises, valve 6 (K) opens and liquid is sucked into the space under the piston. When the small piston is lowered under the influence of liquid pressure, valve 6 (K) closes, and valve 7 (K") opens, and the liquid flows into the large vessel.
The effect of water and gas on a body immersed in them.
Underwater we can easily lift a stone that is difficult to lift in the air. If you put a cork under water and release it from your hands, it will float up. How can these phenomena be explained?
We know (§ 38) that the liquid presses on the bottom and walls of the vessel. And if some solid body is placed inside the liquid, it will also be subject to pressure, just like the walls of the vessel.
Let us consider the forces that act from the liquid on a body immersed in it. To make it easier to reason, let’s choose a body that has the shape of a parallelepiped with bases parallel to the surface of the liquid (Fig.). Forces acting on side faces bodies are equal in pairs and balance each other. Under the influence of these forces, the body contracts. But the forces acting on the upper and lower edges of the body are not the same. The top edge is pressed by force from above F 1 column of liquid high h 1. At the level of the lower edge, the pressure produces a column of liquid with a height h 2. This pressure, as we know (§ 37), is transmitted inside the liquid in all directions. Consequently, on the lower face of the body from bottom to top with force F 2 presses a column of liquid high h 2. But h 2 more h 1, therefore, the force modulus F 2 more power module F 1. Therefore, the body is pushed out of the liquid with force F Vt, equal to the difference in forces F 2 - F 1, i.e.
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But S·h = V, where V is the volume of the parallelepiped, and ρ f ·V = m f is the mass of liquid in the volume of the parallelepiped. Hence, F out = g m w = P w, i.e. buoyant force is equal to the weight of the liquid in the volume of the body immersed in it(the buoyant force is equal to the weight of the liquid of the same volume as the volume of the body immersed in it). The existence of a force pushing a body out of a liquid is easy to detect experimentally. In the picture A shows a body suspended from a spring with an arrow pointer at the end. The arrow marks the tension of the spring on the tripod. When the body is released into the water, the spring contracts (Fig. b). The same contraction of the spring will be obtained if you act on the body from bottom to top with some force, for example, press with your hand (lift). Therefore, experience confirms that a body in a liquid is acted upon by a force that pushes the body out of the liquid. As we know, Pascal's law also applies to gases. That's why bodies in gas are subject to a force that pushes them out of the gas. Under the influence of this force, the balloons rise upward. The existence of a force pushing a body out of a gas can also be observed experimentally. We hang a glass ball or a large flask closed with a stopper from the shortened scale pan. The scales are balanced. Then a wide vessel is placed under the flask (or ball) so that it surrounds the entire flask. The vessel is filled with carbon dioxide, the density of which is greater than the density of air (therefore carbon dioxide falls down and fills the vessel, displacing air from it). In this case, the balance of the scales is disturbed. The cup with the suspended flask rises upward (Fig.). A flask immersed in carbon dioxide experiences a greater buoyancy force than the force that acts on it in air. The force that pushes a body out of a liquid or gas is directed opposite to the force of gravity applied to this body. Therefore, prolkosmos). This is precisely why in water we sometimes easily lift bodies that we have difficulty holding in the air. A small bucket and a body are suspended from the spring cylindrical(Fig., a). An arrow on the tripod marks the stretch of the spring. It shows the weight of the body in the air. Having lifted the body, a casting vessel filled with liquid to the level of the casting tube is placed under it. After which the body is completely immersed in the liquid (Fig., b). At the same time part of the liquid, the volume of which is equal to the volume of the body, is poured out from the pouring vessel into the glass. The spring contracts and the spring pointer rises, indicating a decrease in body weight in the fluid. IN in this case In addition to gravity, another force acts on the body, pushing it out of the liquid. If liquid from a glass is poured into the upper bucket (i.e., the liquid that was displaced by the body), then the spring pointer will return to its initial position (Fig., c).
Based on this experience it can be concluded that the force pushing out a body completely immersed in a liquid is equal to the weight of the liquid in the volume of this body . We received the same conclusion in § 48. If a similar experiment were performed with a body immersed in some gas, it would show that the force pushing a body out of a gas is also equal to the weight of the gas taken in the volume of the body . The force that pushes a body out of a liquid or gas is called Archimedean force, in honor of the scientist Archimedes , who first pointed out its existence and calculated its value. So, experience has confirmed that the Archimedean (or buoyant) force is equal to the weight of the liquid in the volume of the body, i.e. F A = P f = g m and. The mass of liquid mf displaced by a body can be expressed through its density ρf and the volume of the body Vt immersed in the liquid (since Vf - the volume of liquid displaced by the body is equal to Vt - the volume of the body immersed in the liquid), i.e. m f = ρ f ·V t. Then we get: F A= g·ρ and · V T Consequently, the Archimedean force depends on the density of the liquid in which the body is immersed and on the volume of this body. But it does not depend, for example, on the density of the substance of the body immersed in the liquid, since this quantity is not included in the resulting formula. Let us now determine the weight of a body immersed in a liquid (or gas). Since the two forces acting on the body in this case are directed in opposite directions (the force of gravity is downward, and the Archimedean force is upward), then the weight of the body in the liquid P 1 will be less weight bodies in vacuum P = g m on Archimedean force F A = g m w (where m g - mass of liquid or gas displaced by the body). Thus, if a body is immersed in a liquid or gas, then it loses as much weight as the liquid or gas it displaced weighs. Example. Determine the buoyant force acting on a stone with a volume of 1.6 m 3 in sea water. Let's write down the conditions of the problem and solve it. When the floating body reaches the surface of the liquid, then with its further upward movement the Archimedean force will decrease. Why? But because the volume of the part of the body immersed in the liquid will decrease, and the Archimedean force is equal to the weight of the liquid in the volume of the part of the body immersed in it. When the Archimedean force becomes equal to the force of gravity, the body will stop and float on the surface of the liquid, partially immersed in it. The resulting conclusion can be easily verified experimentally. Pour water into the drainage vessel to the level of the drainage tube. After this, we will immerse the floating body in the vessel, having previously weighed it in the air. Having descended into water, a body displaces a volume of water equal to the volume of the part of the body immersed in it. Having weighed this water, we find that its weight (Archimedean force) is equal to the force of gravity acting on a floating body, or the weight of this body in the air. Having done the same experiments with any other bodies floating in different liquids - water, alcohol, salt solution, you can be sure that if a body floats in a liquid, then the weight of the liquid displaced by it is equal to the weight of this body in the air. It's easy to prove that if the density of a solid solid is greater than the density of a liquid, then the body sinks in such a liquid. A body with a lower density floats in this liquid. A piece of iron, for example, sinks in water but floats in mercury. A body whose density is equal to the density of the liquid remains in equilibrium inside the liquid. Ice floats on the surface of water because its density is less than the density of water. The lower the density of the body compared to the density of the liquid, the less part of the body is immersed in the liquid . At equal densities bodies and liquids a body floats inside a liquid at any depth. Two immiscible liquids, for example water and kerosene, are located in a vessel in accordance with their densities: in the lower part of the vessel - denser water (ρ = 1000 kg/m3), on top - lighter kerosene (ρ = 800 kg/m3) . The average density of living organisms inhabiting the aquatic environment differs little from the density of water, so their weight is almost completely balanced by the Archimedean force. Thanks to this, aquatic animals do not need such strong and massive skeletons as terrestrial ones. For the same reason, the trunks of aquatic plants are elastic. The swim bladder of a fish easily changes its volume. When a fish, with the help of muscles, descends to a greater depth, and the water pressure on it increases, the bubble contracts, the volume of the fish’s body decreases, and it is not pushed up, but floats in the depths. Thus, the fish can regulate the depth of its dive within certain limits. Whales regulate the depth of their dive by decreasing and increasing their lung capacity. Sailing of ships.Vessels sailing on rivers, lakes, seas and oceans are built from different materials with different densities. The hull of ships is usually made from steel sheets. All internal fastenings that give ships strength are also made of metals. Used to build ships various materials, having both higher and lower densities compared to water. How do ships float, take on board and carry large cargo? An experiment with a floating body (§ 50) showed that the body displaces so much water with its underwater part that the weight of this water is equal to the weight of the body in the air. This is also true for any vessel. The weight of water displaced by the underwater part of the vessel is equal to the weight of the vessel with the cargo in the air or the force of gravity acting on the vessel with the cargo. The depth to which a ship is immersed in water is called draft . The maximum permissible draft is marked on the ship's hull with a red line called waterline (from Dutch. water- water). The weight of water displaced by a ship when submerged to the waterline, equal to the force of gravity acting on the loaded ship, is called the ship's displacement. Currently, ships with a displacement of 5,000,000 kN (5 × 10 6 kN) or more are being built for the transportation of oil, that is, having a mass of 500,000 tons (5 × 10 5 t) or more together with the cargo. If we subtract the weight of the vessel itself from the displacement, we get the carrying capacity of this vessel. The carrying capacity shows the weight of the cargo carried by the ship. Shipbuilding existed in Ancient Egypt, Phenicia (it is believed that the Phoenicians were one of the best shipbuilders), and Ancient China. In Russia, shipbuilding originated at the turn of the 17th and 18th centuries. Mostly warships were built, but it was in Russia that the first icebreaker, ships with an internal combustion engine, and the nuclear icebreaker Arktika were built. Aeronautics.
Drawing describing the balloon of the Montgolfier brothers from 1783: “View and exact dimensions of the Balloon Globe“who was the first.” 1786 Since ancient times, people have dreamed of the opportunity to fly above the clouds, to swim in the ocean of air, as they swam on the sea. For aeronautics At first, they used balloons that were filled with either heated air, hydrogen or helium. In order for a balloon to rise into the air, it is necessary that the Archimedean force (buoyancy) F A acting on the ball was greater than the force of gravity F heavy, i.e. F A > F heavy As the ball rises upward, the Archimedean force acting on it decreases ( F A = gρV), since the density upper layers atmosphere is less than that of the Earth's surface. To rise higher, a special ballast (weight) is dropped from the ball and this lightens the ball. Eventually the ball reaches its maximum lifting height. To release the ball from its shell, a portion of the gas is released using a special valve. In the horizontal direction, a balloon moves only under the influence of wind, which is why it is called balloon (from Greek aer- air, stato- standing). Not so long ago, huge balloons were used to study the upper layers of the atmosphere and stratosphere - stratospheric balloons . Before we learned how to build large planes for air transportation of passengers and cargo, controlled balloons were used - airships. They have an elongated shape; a gondola with an engine is suspended under the body, which drives the propeller. The balloon not only rises up on its own, but can also lift some cargo: the cabin, people, instruments. Therefore, in order to find out what kind of load a balloon can lift, it is necessary to determine it lift. Let, for example, let a balloon with a volume of 40 m 3 filled with helium be launched into the air. The mass of helium filling the shell of the ball will be equal to: This means that this ball can lift a load weighing 520 N - 71 N = 449 N. This is its lifting force. A balloon of the same volume, but filled with hydrogen, can lift a load of 479 N. This means that its lifting force is greater than that of a balloon filled with helium. But helium is still more often used, since it does not burn and is therefore safer. Hydrogen is a flammable gas. It is much easier to lift and lower a balloon filled with hot air. To do this, a burner is located under the hole located in the lower part of the ball. With the help gas burner you can regulate the temperature of the air inside the ball, and therefore its density and buoyant force. To make the ball rise higher, it is enough to heat the air in it more strongly by increasing the burner flame. As the burner flame decreases, the air temperature in the ball decreases and the ball goes down. You can select a ball temperature at which the weight of the ball and the cabin will be equal to the buoyant force. Then the ball will hang in the air, and it will be easy to make observations from it. As science developed, significant changes occurred in aeronautical technology. It became possible to use new shells for balloons, which became durable, frost-resistant and lightweight. Advances in the field of radio engineering, electronics, and automation have made it possible to design unmanned balloons. These balloons are used to study air currents, for geographical and biomedical research in the lower layers of the atmosphere. Daily questions about why pumps cannot suck up liquid from a depth of more than 9 meters prompted me to write an article about this. No one could explain what was going on here until Galileo’s student E. Toricelli suggested that the water in the system rises under the influence of the gravity of the atmosphere, which presses on the surface of the lake. A column of water 10.3 m high exactly balances this pressure, and therefore the water does not rise higher. Toricelli took a glass tube with one end sealed and the other open and filled it with mercury. Then he closed the hole with his finger and, turning the tube over, lowered its open end into a vessel filled with mercury. The mercury did not pour out of the tube, but only dropped a little.
In the same way, if in an experiment with mercury you pour water into the tube instead, the column of water will be 10.3 meters high. This is why they don’t make water barometers, because... they would be too bulky.
The pressure of a liquid column (P) is equal to the product of the acceleration of gravity (g), the density of the liquid (ρ) and the height of the liquid column:
Atmospheric pressure at sea level (P) is assumed to be equal to 1 kg/cm2 (100 kPa). The density of water at a temperature of 20°C is 1000 kg/m3. From this formula it is clear that the lower the atmospheric pressure (P), the lower the height the liquid can rise (i.e., the higher above sea level, for example in the mountains, the lower the depth the pump can suck from). For example, the same mercury, with ideal conditions, can be lifted from a height of no more than 760 mm. So, what conclusions can be drawn from all this: where P is atmospheric pressure, is the density of the liquid. g – gravitational acceleration, x – loss value (m). Note: The formula can be used to calculate the suction lift at normal conditions and temperatures up to +30°C. For example, when the liquid temperature increases to +60°C, the suction height decreases by almost half. And the most interesting thing is that we all went through all this in a physics lesson while studying the topic “atmospheric pressure”. The calculator below is designed to calculate an unknown quantity from given values using the formula for the pressure of a liquid column. The calculator allows you to find
Deriving formulas for all cases is trivial. For density, the default value is the density of water, for the acceleration of gravity - the earth's acceleration, and for pressure - a value equal to one atmosphere of pressure. A little theory, as usual, under the calculator. pressure density height acceleration of gravity Pressure in liquid, Pa Liquid column height, m Liquid density, kg/m3 Gravity acceleration, m/s2 Hydrostatic pressure - pressure of the water column above the conventional level. The formula for hydrostatic pressure is derived quite simply From this formula it is clear that pressure does not depend on the area of the vessel or its shape. It depends only on the density and height of the column of a particular liquid. From which it follows that by increasing the height of the vessel, we can create quite high blood pressure. This also leads to the phenomenon of hydrostatic paradox. Hydrostatic paradox- a phenomenon in which the force of weight pressure of a liquid poured into a vessel at the bottom of the vessel may differ from the weight of the liquid poured. In vessels with a cross-section increasing upward, the pressure force on the bottom of the vessel is less than the weight of the liquid; in vessels with a cross-section decreasing upward, the pressure force on the bottom of the vessel more weight liquids. The force of liquid pressure on the bottom of the vessel is equal to the weight of the liquid only for a cylindrical vessel.
In the picture above, the pressure at the bottom of the vessel is the same in all cases and does not depend on the weight of the liquid poured, but only on its level. The reason for the hydrostatic paradox is that the liquid presses not only on the bottom, but also on the walls of the vessel. Fluid pressure at inclined walls has a vertical component. In a vessel that expands upward, it is directed downward; in a vessel that narrows upward, it is directed upward. The weight of the liquid in the container will be equal to the sum vertical components of liquid pressure over the entire internal area of the vessel Plumbing, it would seem, does not give much reason to delve into the jungle of technologies, mechanisms, or engage in scrupulous calculations for building the most complex schemes. But such a vision is a superficial look at plumbing. The real plumbing industry is in no way inferior in complexity to the processes and, like many other industries, requires professional approach. In turn, professionalism is a solid store of knowledge on which plumbing is based. Let’s dive (albeit not too deeply) into the plumbing training stream in order to get one step closer to the professional status of a plumber. The fundamental basis of modern hydraulics was formed when Blaise Pascal discovered that the action of fluid pressure is constant in any direction. The action of liquid pressure is directed at right angles to the surface area. If a measuring device (pressure gauge) is placed under a layer of liquid at a certain depth and its sensitive element is directed in different directions, the pressure readings will remain unchanged in any position of the pressure gauge. That is, the fluid pressure does not depend in any way on the change in direction. But the fluid pressure at each level depends on the depth parameter. If the pressure meter is moved closer to the surface of the liquid, the reading will decrease. Accordingly, when diving, the measured readings will increase. Moreover, under conditions of doubling the depth, the pressure parameter will also double. Pascal's law clearly demonstrates the effect of water pressure in the most familiar conditions for modern life Obviously, when speed becomes a factor, direction comes into play. A force tied to speed must also have a direction. Therefore, Pascal's law, as such, does not apply to the dynamic power factors of fluid flow.  The speed of flow depends on many factors, including the layer-by-layer separation of the liquid mass, as well as resistance created by various factors Dynamic factors of inertia and friction are tied to static factors. The velocity head and pressure loss are tied to the hydrostatic head of the liquid. However, part of the velocity head can always be converted into static pressure. The force, which can be caused by pressure or pressure when handling liquids, is necessary to start the movement of a body if it is at rest, and is present in one form or another when. Therefore, whenever the speed of movement of a fluid is set, part of its initial static pressure is used to organize this speed, which subsequently exists as a pressure speed. Volume and flow rateThe volume of fluid passing through a certain point at a given time is considered as flow volume or flow rate. Flow volume is usually expressed in liters per minute (L/min) and is related to the relative pressure of the fluid. For example, 10 liters per minute at 2.7 atm. Flow rate (fluid speed) is defined as average speed, at which the fluid moves past given point. Typically expressed in meters per second (m/s) or meters per minute (m/min). The flow rate is important factor when calibrating hydraulic lines.  The volume and speed of fluid flow are traditionally considered “related” indicators. With the same transmission volume, the speed may vary depending on the cross-section of the passage Volume and flow rate are often considered simultaneously. All other things being equal (assuming the input volume remains constant), the flow rate increases as the cross-section or size of the pipe decreases, and the flow rate decreases as the cross-section increases. Thus, a slowdown in flow speed is observed in wide parts of pipelines, and in narrow places, on the contrary, the speed increases. At the same time, the volume of water passing through each of these control points remains unchanged. Bernoulli's principleThe well-known Bernoulli principle is built on the logic that a rise (fall) in the pressure of a fluid fluid is always accompanied by a decrease (increase) in speed. Conversely, an increase (decrease) in fluid velocity leads to a decrease (increase) in pressure. This principle underlies a number of common plumbing phenomena. As a trivial example, Bernoulli's principle is responsible for causing the shower curtain to "retract inward" when the user turns on the water. The pressure difference between the outside and inside causes a force on the shower curtain. With this forceful effort, the curtain is pulled inward. To others a clear example is a perfume bottle with a spray nozzle when an area is created low pressure due to high air speed. And the air carries the liquid with it.  Bernoulli's principle for an aircraft wing: 1 - low pressure; 2 - high pressure; 3 — fast flow; 4 — slow flow; 5 - wing Bernoulli's principle also shows why windows in a house tend to break spontaneously during hurricanes. In such cases it is extremely high speed air outside the window leads to the fact that the pressure outside becomes much less than the pressure inside, where the air remains practically motionless. A significant difference in force simply pushes the windows outward, causing the glass to break. So when it gets closer strong hurricane Basically, you should open the windows as wide as possible to equalize the pressure inside and outside the building. And a couple more examples when Bernoulli’s principle operates: the rise of an airplane with subsequent flight due to the wings and the movement of “curve balls” in baseball. In both cases, a difference in the speed of air passing past the object from above and below is created. For airplane wings, the difference in speed is created by the movement of the flaps; in baseball, it is the presence of a wavy edge. Home Plumber Practice
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