Lesson: Pascal's Law

After studying this lesson, you will know how fluids transfer the pressure exerted on them.

Topic: Pressure of solids, liquids and gases

Lesson: Pascal's Law

1. Recall how the molecules of matter move

Before proceeding directly to the study of Pascal's law of gas pressure, let's recall how the molecules of solids, liquids and gases move (Fig. 1).

Rice. 1. Molecular structure of solid, liquid and gaseous bodies

The molecules of solids oscillate around their equilibrium positions, while the molecules of liquids and gases have relative freedom to move. They can move relative to each other. It is this feature in the movement of liquid and gas molecules that allows the pressure exerted on a liquid or gas to be transmitted not only in the direction of the force, but in all directions. Let us analyze this process in more detail, stage by stage.

2. Transmission of pressure by gases and liquids

Consider a cylinder containing a gas (for example, air) and which is closed by a movable piston. This may be, for example, a medical syringe, the tip of which was closed with a tube sealed at one end so that air could not escape from the syringe (Fig. 2).

Rice. 2. Demonstration of air compressibility

If you act on the syringe plunger with some force, it will move down. Consequently, the volume of gas contained in the syringe will decrease. On the other hand, by increasing the force applied to the piston, we increase the pressure exerted on the gas. What happens in this case to the gas pressure in other parts of the syringe that are not adjacent to the piston?

Rice. 3. Distribution of gas molecules under the moving piston

The gas molecules in the cylinder move randomly, but on average they are evenly distributed over its volume (Fig. 3a). The pressure of the gas on the walls, the bottom of the cylinder and on the piston is due to the impacts of the molecules.

Move the piston down (Fig. 3b). At the first moment, the distance between the gas molecules in the immediate vicinity of the piston will decrease, the molecular layers adjacent to the piston will approach each other. The number of hits of molecules on the piston will increase, that is, the pressure of the gas on the piston will increase. In the remaining parts of the cylinder, the average distance between the molecules will not change, since it takes some time for the molecules to move.

After some very short time, the gas molecules, due to collisions with each other and with the walls of the vessel, will be redistributed so that the average distance between them will again become the same in all parts of the vessel. However, since the total number of molecules in the sealed cylinder has not changed, and the volume of the cylinder has become smaller, now the average distance between molecules will now be smaller than before the piston was moved (Fig. 3c). In other words, the density of the gas molecules will increase. And this, in turn, leads to an increase in the number of impacts of molecules on the walls of the vessel. in all parts of the vessel, and not just near the piston. Accordingly, the pressure exerted on the gas by the piston is transmitted to all points of the gas.

An analysis of the behavior of liquid molecules shows that liquids behave in the same way.

3. Pascal's Law

The pressure exerted on a liquid or gas is transmitted unchanged to any point in the liquid or gas.

This statement is called Pascal's law.

The validity of Pascal's law can be demonstrated using an apparatus called Pascal's ball. It is a ball with small holes located over its entire surface. The ball is connected to a cylinder closed by a movable piston. The device is filled with water or smoke. When a force is applied to the piston, liquid or smoky air flows out of all the holes of the ball, and not just from those located opposite the piston (Fig. 4).

Rice. 4. Pascal's ball

4. Applications of Pascal's Law

The property of liquids and gases, described by Pascal's law, is widely used in technology and in our everyday life. For example, if Pascal's law was not fulfilled, it would be impossible to create a water supply system, oil and gas pipelines. After all, water and gas pipes on the way to consumers experience a large number of bends, but, nevertheless, the pressure created by pumps that pump water, oil or gas is transmitted unchanged from the pump to destinations. Train braking systems on railways or door opening systems on electric trains and subways also work thanks to Pascal's law.

Try to imagine what would happen if there were sand instead of liquid or gas in the pipes!.. After all, it does not obey Pascal's law.

Bibliography

1. A. V. Peryshkin, Physics. 7 cells - 14th ed., stereotype. – M.: Bustard, 2010.

2. Peryshkin A. V. Collection of problems in physics, 7–9 cells: 5th ed., stereotype. - M: Publishing house "Exam", 2010.

3. Lukashik V. I., Ivanova E. V. Collection of problems in physics for grades 7–9 of educational institutions. – 17th ed. - M .: Education, 2004.

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In total there are 6 presentations in the topic

That's what it is Pascal's law.

According to this law, the pressure inside liquids and gases spreads in all possible directions. Therefore, liquids and gases exert pressure in all directions: left, right, and even up! This is confirmed by experiments. Let's consider some of them.

Take a glass tube and a light disk on a thread (Fig. "a"). Pulling the thread, we get a vessel with a falling bottom (Fig. "b"). Immerse this vessel in a wide glass of water. Surprisingly, now the bottom will not fall off, even if the thread is not pulled (Fig. "c").

Q. Why do you think this is happening?

A. This happens because the upper layers of water in the glass create pressure on the underlying layers, including the layer of water under the disk. According to Pascal's law, pressure is transmitted through this layer and acts on the disk from the bottom up. The force of this pressure supports the disk and presses it against the edges of the glass tube.

Let's continue the experiment. Pour so much tinted water into the tube so that its level is lower than that of the water in the glass (Fig. "d"). We will see that the disk does not fall off.

Q. Why won't the disc fall off?

A. This is because there is more pressure on the disk from below than from above. Increase the height of the colored water layer. The disc will fall off (Fig. "e"). This means that the pressure on the disk from above, created by the colored water, exceeded the pressure from below, created by the water in the glass.

Pascal's law has an interesting consequence: regardless of the shape and size of the vessel, the pressure inside the liquid at the same depth is the same.

Let's prove this statement.

Let the considered "vessel" be a sea bay with an underwater cave. Take a look at the picture. It would seem that the water pressure in the cave is less than the pressure in the open sea. However, if this were the case, then under the action of a greater pressure, water from the sea would rush into the cave, and the water level in the sea would begin to drop. Incredible, right?

Therefore, since the water at the entrance to the cave (and also in the sea) remains at rest, then the pressure of the water in the cave is equal to the pressure of the water in the open sea.

Q. Do solids obey Pascal's law?

A. No, because in solids, the mobility of molecules is limited.

That's right, if we put a heavy object on the table, then the weight of this object creates pressure only on the area under this object, i.e. only in the direction of the force.

Q. What are the main conclusions you can draw?

A. Liquid and gas molecules are very mobile.

Due to the mobility of the molecules of liquid and gas, they transmit the pressure produced on them to all points without changing its value.

Rigid bodies do not obey Pascal's law.

Transmission of pressure by gases, liquids and solids. Pascal's law and its application in hydraulic machines

Solid bodies transmit the pressure produced on them in the direction of the force. To determine the pressure (p) need force (F) acting perpendicular to the surface, divided by the surface area ()- Pressure is measured in Pascals: 1 Pa = 1 N/m 2 . The pressure exerted on the liquid and gas is transmitted not only in the direction of the force, but to every point of the liquid or gas. This is due to the mobility of gas and liquid particles. Pascal's law. The pressure exerted on a liquid or gas is transmitted unchanged to each point of the liquid or gas. The law is confirmed by experiments with Pascal's ball and the operation of hydraulic machines. Let us dwell on the operation of this machine (see Fig.). F1 and F2- forces acting on the pistons, S1 and S2- area of ​​the pistons. Pressure under the small piston. under the big piston. According to Pascal's law p 1 \u003d p 2, i.e. i.e. the pressure at all points of a fluid at rest is the same, or, from where. The machine gives a gain in strength as many times as the area of ​​the large piston is greater than the area of ​​the small one. This is seen in the operation of a hydraulic press used to make steel machine shafts, railway wheels, or to squeeze oil in oil mills, and in hydraulic jacks.

Atmosphere pressure. Instruments for measuring atmospheric pressure. The air shell of the Earth and its role in human life

Atmosphere- the air shell around the Earth, extending to a height of several thousand kilometers. Due to the action of gravity, the air layer adjacent to the Earth is compressed the most and transmits the pressure produced on it in all directions. As a result of this, the earth's surface and the bodies on it experience atmospheric pressure. First time measured Atmosphere pressure Italian physicist Torricelli using a glass tube sealed at one end and filled with mercury (see Fig.). The pressure in the tube at the level aa created by the gravity of a mercury column height h = 760 mm, at the same time, atmospheric pressure acts on the surface of the mercury in the cup. These pressures balance each other. Since airless space remains in the upper part of the tube after lowering the mercury column, by measuring the height of the column, you can determine the numerical value of atmospheric pressure using the formula: p == 9.8 N / kg × 13,600 kg / m 3 × 0.76 m \u003d 101,300 Pa \u003d 1013 GPa. Instruments for measuring atmospheric pressure are mercury barometer and barometraneroid. The principle of operation of the latter is based on compressing a hollow corrugated metal box and transferring its deformation through a system of levers to an arrow-pointer. The aneroid barometer has two scales: the inner one is graduated in mm Hg. Art. (1 mm Hg. Art. = 133.3 Pa), external - in kilopascals. Knowing the atmospheric pressure is very important for predicting the weather for the coming days. Troposphere(lower layer of the atmosphere) is due to diffusion a homogeneous mixture of nitrogen, oxygen, carbon dioxide and water vapor. This mixture of gases supports the normal functioning of all life on Earth. Harmful emissions into the atmosphere pollute the environment. For example, the accident at the Chernobyl nuclear power plant, accidents on nuclear submarines, atmospheric emissions from industrial enterprises, etc.

Solid bodies transmit the pressure produced on them in the direction of the force. To determine the pressure (p) need force (F) , acting perpendicular to the surface, divided by the surface area () - Pressure is measured in Pascals: 1 Pa = 1 N/m 2 . The pressure exerted on the liquid and gas is transmitted not only in the direction of the force, but to every point of the liquid or gas. This is due to the mobility of gas and liquid particles. Pascal's law.The pressure exerted on a liquid or gas is transmitted unchanged to each point of the liquid or gas. The law is confirmed by experiments with Pascal's ball and the operation of hydraulic machines. Let us dwell on the operation of this machine (see Fig.). F 1 and F 2 - forces acting on the pistons, S 1 and S 2 - area of ​​the pistons. pressure under the small piston. under the big piston. According to Pascal's law p 1 =p 2 , t. i.e. the pressure at all points of the fluid at rest is the same, or , whence. The machine gives a gain in strength as many times as the area of ​​the large piston is greater than the area of ​​the small one. This is seen in the operation of a hydraulic press used to make steel machine shafts, railway wheels, or to squeeze oil in oil mills, and in hydraulic jacks.

12. Atmospheric pressure. Instruments for measuring atmospheric pressure. The air shell of the Earth and its role in human life

Atmosphere- the air shell around the Earth, extending to a height of several thousand kilometers. Due to the action of gravity, the air layer adjacent to the Earth is compressed the most and transmits the pressure produced on it in all directions. As a result of this, the earth's surface and the bodies on it experience atmospheric pressure. First time measured Atmosphere pressure Italian physicist Torricelli using a glass tube sealed at one end and filled with mercury (see fig.). The pressure in the tube at the level aa created by the gravity of a mercury column height h = 760 mm, at the same time, atmospheric pressure acts on the surface of the mercury in the cup. These pressures balance each other. Since airless space remained in the upper part of the tube after lowering the mercury column, by measuring the height of the column, you can determine the numerical value of atmospheric pressure using the formula: p == 9.8 N / kg H 13,600 kg / m 3 H 0.76 m \u003d 101,300 Pa \u003d 1013 GPa. Instruments for measuring atmospheric pressure are mercury barometer and barometraneroid. The principle of operation of the latter is based on compressing a hollow corrugated metal box and transferring its deformation through a system of levers to an arrow-pointer. The aneroid barometer has two scales: the inner one is graduated in mm Hg. Art. (1 mm Hg. Art. = 133.3 Pa), external - in kilopascals. Knowing the atmospheric pressure is very important for predicting the weather for the coming days. Troposphere(lower layer of the atmosphere) is due to diffusion a homogeneous mixture of nitrogen, oxygen, carbon dioxide and water vapor. This mixture of gases supports the normal functioning of all life on Earth. Harmful emissions into the atmosphere pollute the environment. For example, the accident at the Chernobyl nuclear power plant, accidents on nuclear submarines, emissions into the atmosphere of industrial enterprises, etc.