Pascal's law is valid for solids why. Pascal's Law (Basic Equation of Hydrostatics)
The famous French philosopher, mathematician and physicist of the 17th century Blaise Pascal made an important contribution to the development of modern science. One of his main achievements was the formulation of the so-called Pascal's law, which is associated with the property of fluid substances and the pressure created by them. Let's take a closer look at this law.
Brief biography of the scientist
Blaise Pascal was born on June 19, 1623 in Clermont-Ferrand, France. His father was a vice president of tax collection and a mathematician, and his mother belonged to the bourgeois class. From a young age, Pascal began to show interest in mathematics, physics, literature, languages, and religious teachings. He invented a mechanical calculator that could perform addition and subtraction. Spent a lot of time studying physical properties fluid bodies, as well as the development of the concepts of pressure and vacuum. One of the important discoveries of the scientist was the principle that bears his name - Pascal's law. Blaise Pascal died in 1662 in Paris due to paralysis of the legs, a disease that accompanied him from 1646.
The concept of pressure
Before considering Pascal's law, let's deal with such physical quantity like pressure. It is a scalar physical quantity denoting the force that acts on a given surface. When a force F begins to act on a surface of area A perpendicular to it, then the pressure P is calculated using the following formula: P = F / A. The pressure is measured in the International System of Units SI in pascals (1 Pa = 1 N / m 2), that is, in honor of Blaise Pascal, who devoted many of his works to the issue of pressure.
If the force F acts on a given surface A not perpendicularly, but at some angle α to it, then the expression for pressure will take the form: P = F*sin(α)/A, in this case F*sin(α) is the perpendicular component force F to surface A.
Pascal's Law
In physics, this law can be formulated as follows:
The pressure applied to a practically incompressible fluid substance, which is in equilibrium in a vessel having non-deformable walls, is transmitted in all directions with the same intensity.
You can verify the correctness of this law as follows: you need to take a hollow sphere, make holes in it in various places, supply this sphere with a piston and fill it with water. Now, by applying pressure to the water with the help of a piston, you can see how it pours out of all the holes at the same speed, which means that the water pressure in the area of \u200b\u200beach hole is the same.
Liquids and gases
Pascal's law is formulated for fluid substances. Liquids and gases fall under this concept. However, unlike gases, the molecules that form a liquid are located close to each other, which causes liquids to have such a property as incompressibility.
Due to the property of the incompressibility of a liquid, when a finite pressure is created in a certain volume of it, it is transmitted in all directions without loss of intensity. This is exactly what Pascal's principle is about, which is formulated not only for fluid, but also for incompressible substances.
Considering in this light the question of "gas pressure and Pascal's law," it should be said that gases, unlike liquids, are easily compressed without maintaining volume. This leads to the fact that when an external pressure is applied to a certain volume of gas, it is also transmitted in all directions and directions, but at the same time it loses intensity, and its loss will be the stronger, the lower the density of the gas.
Thus, Pascal's principle is valid only for liquid media.
Pascal's principle and the hydraulic machine
Pascal's principle is applied in various hydraulic devices. In order to use Pascal's law in these devices, the following formula is valid: P \u003d P 0 + ρ * g * h, here P is the pressure that acts in the liquid at a depth h, ρ is the density of the liquid, P 0 is the pressure applied to the surface of the liquid, g (9.81 m / s 2) - free fall acceleration near the surface of our planet.
The principle of operation of a hydraulic machine is as follows: two cylinders that have different diameters are connected to each other. This complex vessel is filled with some liquid, such as oil or water. Each cylinder is provided with a piston so that no air remains between the cylinder and the surface of the liquid in the vessel.
Suppose that a certain force F 1 acts on a piston in a cylinder with a smaller cross section, then it creates pressure P 1 = F 1 /A 1. According to Pascal's law, the pressure P 1 will instantly be transferred to all points of space inside the liquid in accordance with the above formula. As a result, a pressure P 1 with a force F 2 = P 1 * A 2 = F 1 * A 2 / A 1 will also act on a piston with a large cross section. The force F 2 will be directed opposite to the force F 1, that is, it will tend to push the piston up, while it will be greater than the force F 1 exactly as many times as the cross-sectional area of the machine's cylinders differs.
Thus, Pascal's law allows you to lift large loads with the help of small balancing forces, which is a kind of similarity to Archimedes' lever.
Other applications of Pascal's principle
The considered law is used not only in hydraulic machines, but finds wider application. Below are examples of systems and devices, the operation of which would be impossible if Pascal's law was not valid:
- In the brake systems of cars and in the well-known anti-lock ABS system, which prevents the wheels of the car from blocking during its braking, which helps to avoid skidding and slipping of the vehicle. In addition, the ABS system allows the driver to maintain control in driving vehicle when the latter performs emergency braking.
- In any type of refrigerators and cooling systems, where the working substance is a liquid substance (freon).
Blaise Pascal was a French mathematician, physicist and philosopher who lived in the middle of the seventeenth century. He studied the behavior of liquids and gases, studied pressure.
He noticed that the shape of the vessel had no effect on the pressure of the liquid inside it. He also formulated the principle: liquids and gases transmit equally in all directions the pressure exerted on them.
This principle is called Pascal's law for liquids and gases.
It must be understood that this law did not take into account the force of gravity acting on the liquid. In fact, The fluid pressure increases with depth due to attraction towards the Earth, and this is hydrostatic pressure.
To calculate its value, the formula is used: 
is the pressure of the liquid column.
- ρ is the density of the liquid;
- g - free fall acceleration;
- h - depth (height of the liquid column).
The total fluid pressure at any depth is the sum of the hydrostatic pressure and the pressure associated with external compression: 
where p0 is the external pressure, for example, of a piston in a vessel filled with water.
Application of Pascal's law in hydraulics
Hydraulic systems use incompressible fluids such as oil or water to transfer pressure from one point to another within the fluid in a forceful manner. Hydraulic devices are used for crushing solids, in the press. In aircraft, hydraulics are installed in the brake systems and landing gear.
Since Pascal's law is also valid for gases, there are pneumatic systems in technology that use air pressure.
Archimedean strength. Bodies floating condition
Knowing the Archimedean force (in other words, buoyancy) is important when trying to understand why some bodies float while other bodies sink.
Consider an example. The man is in the pool. When he is completely submerged under water, he can easily perform somersaults, do somersaults or jump very high. On land, such tricks are much more difficult to perform.
Such a situation in the pool is possible due to the fact that the Archimedean force acts on a person in water. In a liquid, the pressure increases with depth (this is also true for a gas). When the body is completely under water, the fluid pressure from below the body prevails over the pressure from above, and the body begins to float.
Law of Archimedes
A body in a liquid (gas) is affected by a buoyant force equal in magnitude to the weight of the amount of liquid (gas) that is displaced by the immersed part of the body.
- Ft - gravity;
- Fa - Archimedean force;
- ρzh - density of liquid or gas;
- Vv. and. - the volume of the displaced liquid (gas), equal to the volume of the immersed part of the body;
- Pv. and. is the weight of the displaced fluid.
Sailing condition
- FT> FA - the body is sinking;
- FT< FA - тело поднимается к поверхности до тех пор, пока не окажется в положении равновесия и не начнёт плыть;
- FT \u003d FA - the body is in equilibrium in an aqueous or gaseous environment (floats).
Pascal's law of pressure was discovered in the 17th century by the French scientist Blaise Pascal, after whom it got its name. The wording of this law, its meaning and application in Everyday life discussed in detail in this article.
The essence of Pascal's law
Pascal's law - the pressure that is exerted on a liquid or gas is transmitted to every point of the liquid or gas without change. That is, the transfer of pressure in all directions is the same.
This law is only valid for liquids and gases. The fact is that the molecules of liquid and gaseous substances under pressure behave quite differently from the molecules of solids. Their movement is different. If the molecules of liquid and gas move relatively freely, then the molecules of solids do not have such freedom. They only slightly oscillate, slightly deviating from their original position. And due to the relatively free movement of gas and liquid molecules, they exert pressure in all directions.
Formula and basic value of Pascal's law
The main quantity in Pascal's law is pressure. It is measured in Pascals (Pa). Pressure (P)- attitude force (F), which acts on the surface perpendicular to its Square (S). Hence: P=F/S.
Features of gas and liquid pressure
Being in a closed vessel, the smallest particles of liquids and gases - molecules - hit the walls of the vessel. Since these particles are mobile, from a place with more high pressure they are able to move to a place with low pressure, i.e. within a short time it becomes uniform over the entire surface of the occupied vessel.
For a better understanding of the law, you can conduct an experiment. Let's take balloon and fill it with water. Then we make several holes with a thin needle. The result will not keep you waiting. Water will begin to flow out of the holes, and if the ball is compressed (i.e., pressure is applied), then the pressure of each jet will increase by how many times, regardless of exactly at which point the pressure was applied.
The same experiment can be done with Pascal's ball. It is a round ball with holes available with a piston attached to it.
Rice. 1. Blaise Pascal
The determination of the liquid pressure at the bottom of the vessel occurs according to the formula:
p=P/S=gpSh/s
p=gρ h
- g- acceleration of gravity,
- ρ - liquid density (kg / m3)
- h- depth (height of the liquid column)
- p is the pressure in pascals.
Under water, the pressure depends only on the depth and density of the liquid. That is, in the sea or ocean, the density will be greater with greater immersion.
Rice. 2. Pressure at different depths
Application of the law in practice
Many laws of physics, including Pascal's law, are applied in practice. For example, an ordinary plumbing could not function if this law did not operate in it. After all, the water molecules in the pipe move randomly and relatively freely, which means that the pressure exerted on the walls of the water pipe is the same everywhere. The work of a hydraulic press is also based on the laws of motion and equilibrium of fluids. The press consists of two interconnected cylinders with pistons. The space under the pistons is filled with oil. If the force F 2 acts on the smaller piston with area S 2 , then the force F 1 acts on the larger piston with area S 1 .
Rice. 3. Hydraulic press
You can also experiment with raw and boiled egg. If a sharp object, for example, a long nail, pierces first one and then the other, then the result will be different. A hard-boiled egg will go through a nail, and a raw one will shatter into smithereens, since Pascal's law will apply to a raw egg, but not to a hard one.
Pascal's law says that the pressure at all points of a fluid at rest is the same, that is: F 1 /S 1 \u003d F 2 /S 2, from where F 2 /F 1 \u003d S 2 /S 1.
The force F 2 is as many times greater than the force F 1, how many times the area of the larger piston is greater than the area of the small one.
What have we learned?
The main value of Pascal's law, which is studied in grade 7, is pressure, which is measured in Pascals. Unlike solids, gaseous and liquid substances put pressure on the walls of the vessel in which they are located in the same way. The reason for this is molecules that move freely and randomly in different directions.
Topic quiz
Report Evaluation
Average rating: 4.6. Total ratings received: 550.
The nature of the pressure of a liquid, gas and solid body is different. Although liquid and gas pressures have a different nature, their pressures have one common effect that distinguishes them from solids. This effect, or rather a physical phenomenon, describes Pascal's law.
Pascal's law states that, the pressure produced by external forces to some place in the liquid or gas is transmitted through the liquid or gas without change to any point. This law was discovered by Blaise Pascal in the 17th century.
Pascal's law means that if, for example, you press on the gas with a force of 10 N, and the area of \u200b\u200bthis pressure will be 10 cm 2 (i.e. (0.1 * 0.1) m 2 \u003d 0.01 m 2), then the pressure at the place of application of the force will increase by p \u003d F / S \u003d 10 N / 0.01 m 2 \u003d 1000 Pa, and the pressure in all places of the gas will increase by this amount. That is, the pressure will be transferred unchanged to any point of the gas.
The same is true for liquids. But for solids - no. This is due to the fact that liquid and gas molecules are mobile, and in solids, although they can oscillate, they remain in their place. In gases and liquids, molecules move from an area of higher pressure to an area of lower pressure, so the pressure in the entire volume quickly equalizes.
Pascal's law is confirmed by experience. If very small holes are pierced in a rubber ball filled with water, water will drip through them. If you now press into any one place of the ball, then from all the holes, no matter how far they are from the place where the force is applied, water will flow in streams of approximately the same strength. This suggests that the pressure has spread throughout the volume.
Pascal's law finds practical application. If a certain force is applied to a small surface area of a liquid, then an increase in pressure will occur over the entire volume of the liquid. This pressure can do work to move more surface area.
For example, if an area S 1 is acted upon by a force F 1, then an additional pressure p will be created in the entire volume:
This pressure exerts a force F 2 on the area S 2:
This shows that the larger the area, the greater the force. That is, if we have produced a small force on a small area, then it turns into a large force on a larger area. If in the formula we replace the pressure (p) with the initial force and area, we get the following formula:
F 2 \u003d (F 1 / S 1) * S 2 \u003d (F 1 * S 2) / S 1
Move F 1 to the left side:
F 2 / F 1 \u003d S 2 / S 1
It follows that F 2 is as many times greater than F 1 as S 2 is greater than S 1 .
Based on this gain in strength, hydraulic presses are created. In them, a small force is applied to a narrow piston. As a result, a large force arises in a wide piston, capable of lifting a heavy load or pressing on pressed bodies.
(1623 - 1662)
Pascal's law states: "The pressure exerted on a liquid or gas is transmitted to any point of the liquid or gas equally in all directions."
This statement is explained by the mobility of particles of liquids and gases in all directions.
PASCAL EXPERIENCE
Blaise Pascal demonstrated in 1648 that the pressure of a liquid depends on the height of its column.
He inserted a tube 1 cm2 in diameter and 5 m long into a closed barrel filled with water and, going up to the balcony of the second floor of the house, poured a mug of water into this tube. When the water in it rose to a height of ~ 4 meters, the water pressure increased so much that cracks formed in a strong oak barrel through which water flowed.
Pascal tube
NOW BE CAREFUL!
If you fill vessels of the same size: one with liquid, the other with bulk material (for example, peas), put a solid body close to the walls in the third, put identical circles on the surface of the substance in each vessel, for example, made of wood / they should be adjacent to the walls / , and install weights of the same weight on top,
then how will the pressure of the substance on the bottom and walls in each vessel change? Think! When does Pascal's law work? How will the external pressure of the loads be transferred?
IN WHAT TECHNICAL DEVICES IS PASCAL'S LAW USED?
Pascal's law is the basis for the design of many mechanisms. Look at the pictures, remember!
1. hydraulic presses
The hydraulic multiplier is designed to increase the pressure (p2 > p1, since with the same pressure force S1> S2).
Multipliers are used in hydraulic presses.
2. hydraulic lifts
This is a simplified diagram of a hydraulic lift that is installed on dump trucks.
The purpose of the movable cylinder is to increase the height of the piston. To lower the load, open the crane.
The refueling unit for supplying tractors with fuel operates as follows: the compressor pumps air into a hermetically sealed fuel tank, which enters the tractor tank through a hose.
4. sprayers
In sprayers used to control agricultural pests, the pressure of the air injected into the vessel on the poison solution is 500,000 N/m2. Liquid is sprayed when the faucet is open
5. water supply systems
Pneumatic water supply system. The pump supplies water to the tank, compressing the air cushion, and turns off when the air pressure reaches 400,000 N/m2. The water goes up through the pipes into the rooms. When the air pressure drops, the pump starts up again.
6. water cannons
A jet of water ejected by a water jet at a pressure of 1,000,000,000 N/m2 punches holes in metal ingots and crushes rock in mines. Hydroguns are also equipped with modern fire-fighting equipment.
7. when laying pipelines
The air pressure "inflates" the pipes, which are made in the form of flat metal steel strips welded along the edges. This greatly simplifies the laying of pipelines for various purposes.
8. in architecture
The huge synthetic film dome is supported by a pressure that is only 13.6 N/m2 greater than atmospheric pressure.
9. pneumatic pipelines
Pressure of 10,000 - 30,000 N/m2 works in pneumocontainer pipelines. The speed of trains in them reaches 45 km/h. This type of transport is used to transport bulk and other materials.
Container for transportation of household waste.
YOU CAN DO IT
1. Finish the phrase: "When a submarine dives, the air pressure in it .....". Why?
2. Food for astronauts is made in a semi-liquid form and placed in tubes with elastic walls. With light pressure on the tube, the astronaut extracts the contents from it. What law is manifested in this case?
3. What should be done so that water flows out of the vessel through the tube?
4. In the oil industry, compressed air is used to lift oil to the surface of the earth, which is pumped by compressors into the space above the surface of the oil-bearing layer. What law is manifested in this case? How?
5. Why does an empty paper bag, inflated with air, burst with a crack if you hit it on your hand or on something hard?
6. Why do deep-sea fishes, when pulled to the surface, have a swim bladder sticking out of their mouths?
BOOKSHELF
DO YOU KNOW ABOUT THIS?
What is decompression sickness?
It manifests itself if you rise very quickly from the depths of the water. The pressure of the water decreases sharply and the air dissolved in the blood expands. The resulting bubbles clog the blood vessels, interfering with the movement of blood, and the person may die. Therefore, scuba divers and divers ascend slowly so that the blood has time to carry the resulting air bubbles into the lungs.
How do we drink?
We put a glass or spoon with a liquid to our mouth and “draw” their contents into ourselves. How? Why, in fact, the liquid rushes into our mouths? The reason is this: when we drink, we expand the chest and thereby rarefy the air in the mouth; under the pressure of the outside air, the liquid rushes into the space where the pressure is less, and thus penetrates into our mouth. Here the same thing happens that would happen to the liquid in communicating vessels if we began to rarefy the air above one of these vessels: under the pressure of the atmosphere, the liquid in this vessel would rise. On the contrary, by capturing the neck of the bottle with your lips, you will not “pull” water out of it into your mouth with any effort, since the air pressure in the mouth and above the water is the same. So, we drink not only with the mouth, but also with the lungs; because the expansion of the lungs is the reason that the liquid rushes into our mouth.
Bubble
“Blow a soap bubble,” wrote the great English scientist Kelvin, “and look at it: you can study it all your life without ceasing to learn from it the lessons of physics.”
Soap bubble around a flower
Soapy solution is poured into a plate or onto a tray so that the bottom of the plate is covered with a layer of 2 - 3 mm; a flower or a vase is placed in the middle and covered with a glass funnel. Then, slowly raising the funnel, they blow into its narrow tube - a soap bubble is formed; when this bubble reaches a sufficient size, tilt the funnel, releasing the bubble from under it. Then the flower will be lying under a transparent semicircular cap made of soapy film, shimmering with all the colors of the rainbow.
Several bubbles in each other
A large soap bubble is blown out of the funnel used for the described experiment. Then completely immerse the straw in the soap solution so that only the tip of it, which will have to be taken into the mouth, remains dry, and carefully push it through the wall of the first bubble to the center; then slowly pulling the straw back, not bringing it to the edge, however, they blow out the second bubble enclosed in the first, in it - the third, fourth, etc. It is interesting to observe the bubble when it enters the cold room from a warm room: it apparently decreases in volume and, conversely, swells, getting from a cold room to a warm one. The reason lies, of course, in the contraction and expansion of the air contained within the bubble. If, for example, in frost at - 15 ° C, the volume of the bubble is 1000 cubic meters. cm and from frost it got into a room where the temperature is + 15 ° C, then it should increase in volume by about 1000 * 30 * 1/273 = about 110 cubic meters. cm.
The usual ideas about the fragility of soap bubbles are not entirely correct: with proper handling, it is possible to keep a soap bubble for decades. The English physicist Dewar (famous for his work on liquefying air) kept soap bubbles in special bottles, well protected from dust, drying and shaking; under these conditions, he managed to keep some bubbles for a month or more. Lawrence in America managed to keep soap bubbles under a glass jar for years.