The famous French philosopher, mathematician and physicist of the 17th century Blaise Pascal introduced important contribution in 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 properties 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 French city Clermont-Ferrand. His father was a vice president for tax collection and a mathematician, and his mother belonged to the bourgeois class. WITH youth Pascal began to show interest in mathematics, physics, literature, languages and religious teaching. He invented a mechanical calculator that could perform addition and subtraction operations. Spent a lot of time studying physical properties fluid bodies, as well as the development of pressure and vacuum concepts. One of important discoveries The scientist became a principle that bears his name - Pascal's law. Blaise Pascal died in 1662 in Paris due to paralysis of his legs, an illness that had accompanied him since 1646.
Concept of pressure
Before considering Pascal's law, let's deal with this physical quantity like pressure. It is a scalar physical quantity that denotes 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. Pressure is measured in the International System of Units SI in pascals (1 Pa = 1 N/m2), 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 a certain 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:
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 in the following way: you need to take a hollow sphere, make holes in it in various places, equip this sphere with a piston and fill it with water. Now, by creating pressure on the water using 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 each hole is the same.
Liquids and gases
Pascal's law was 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 incompressibility property of a liquid, when a finite pressure is created in a certain volume, it is transmitted in all directions without loss of intensity. This is exactly what we are talking about in Pascal’s principle, which is formulated not only for fluid, but also for incompressible substances.
Considering the question of “gas pressure and Pascal’s law” in this light, it should be said that gases, unlike liquids, are easily compressed without retaining volume. This leads to the fact that when a certain volume of gas is exposed to external pressure, it is also transmitted in all directions and directions, but at the same time loses intensity, and its loss will be stronger, the lower the gas density.
Thus, Pascal's principle is valid only for liquid media.
Pascal's principle and the hydraulic machine
Pascal's principle is used in various hydraulic devices. In order to use Pascal's law in these devices, the formula is as follows: P = 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) - acceleration free fall near the surface of our planet.
The operating principle 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 equipped with a piston in such a way that no air remains between the cylinder and the surface of the liquid in the vessel.
Suppose that a piston in a cylinder with a smaller cross-section is affected by a certain force F 1, then it creates a pressure P 1 = F 1 / A 1. According to Pascal's law, pressure P 1 will be instantly transmitted to all points in space inside the liquid in accordance with the above formula. As a result, a piston with a large cross-section will also be subject to pressure P 1 with a force F 2 = P 1 * A 2 = F 1 * A 2 / A 1 . The force F2 will be directed opposite to the force F1, that is, it will tend to push the piston upward, and it will be greater than the force F1 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 the Archimedes lever.
Other applications of Pascal's principle
The law under consideration is used not only in hydraulic machines, but is more widely used. Below are examples of systems and devices whose operation would be impossible if Pascal’s law were not valid:
- In the braking systems of cars and in the well-known anti-lock ABS system, which prevents the wheels of the car from locking during braking, which helps to avoid skidding and sliding of the vehicle. In addition, the ABS system allows the driver to maintain control. vehicle when the latter performs emergency braking.
- In any type of refrigerators and cooling systems where the working substance is a liquid substance (freon).
The nature of the pressure of a liquid, gas and solid is different. Although the pressures of liquids and gases are of different natures, their pressures have one similar effect that differentiates them from solids. This effect, or rather a physical phenomenon, is described by Pascal's law.
Pascal's law states that, produced external forces pressure at some point in a 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, a gas is pressed with a force of 10 N, and the area of this pressure is 10 cm 2 (i.e. (0.1 * 0.1) m 2 = 0.01 m 2), then the pressure at the point where the force is applied will increase by p = F/S = 10 N / 0.01 m 2 = 1000 Pa, and the pressure in all places in the gas will increase by this amount. That is, the pressure will be transmitted without changes to any point in the gas.
The same is true for liquids. But for solids - no. This is due to the fact that the molecules of liquid and gas are mobile, and in solids, although they can vibrate, they remain in place. In gases and liquids, molecules move from an area with more high pressure to an area with a lower one, so the pressure throughout the entire volume quickly equalizes.
Pascal's law is confirmed by experience. If you puncture very small holes in a rubber ball filled with water, water will drip through them. If you now press in 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 out in streams of approximately equal strength. This indicates that the pressure has spread throughout the entire volume.
Pascal's law has practical applications. If a certain force is applied to a small surface area of a liquid, an increase in pressure will occur throughout the entire volume of the liquid. This pressure can do work to move larger area surfaces.
For example, if force F1 is applied to area S1, then additional pressure p will be created throughout 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 produce a small force over a small area, then it turns into a large force over a larger area. If in the formula we replace pressure (p) with the original force and area, we get the following formula:
F 2 = (F 1 / S 1) * S 2 = (F 1 * S 2) / S 1
Let's move F 1 to the left side:
F 2 /F 1 = 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 the wide piston, capable of lifting a heavy load or putting pressure on the pressed bodies.
(1623 - 1662)
Pascal's law states: "The pressure exerted on a liquid or gas is transmitted to any point in 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'S EXPERIENCE
In 1648, Blaise Pascal demonstrated that the pressure of a liquid depends on the height of its column.
He inserted a tube with a diameter of 1 cm2 and a length of 5 m 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 the strong oak barrel through which water flowed.
Pascal's tube
NOW BE CAREFUL!
If you fill vessels of the same size: one with liquid, the other with bulk material (for example, peas), place the third one close to the walls solid, on the surface of the substance in each vessel, place identical circles, for example, made of wood / they should be adjacent to the walls /, and place weights of equal weight on top,
then how will the pressure of the substance on the bottom and walls in each vessel change? Think about it! In what case does Pascal's law work? How will the external pressure of the loads be transmitted?
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 pressure (р2 > р1, 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 lifting height of the piston. To lower the load, open the tap.
A refueling unit for supplying tractors with fuel operates as follows: a compressor forces air into a hermetically sealed tank with fuel, which enters the tractor tank through a hose.
4. sprayers
In sprayers used to control agricultural pests, the pressure of the air pumped into the vessel onto the poison solution is 500,000 N/m2. Liquid sprays when the tap 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. Water rises through pipes into the premises. When the air pressure decreases, the pump turns on again.
6. water cannons
A stream of water, ejected by a water cannon under a pressure of 1,000,000,000 N/m2, punches holes in metal blanks and crushes rock in mines. Modern fire-fighting equipment is also equipped with hydrocannons.
7. when laying pipelines
Air pressure “inflates” the pipes, which are made in the form of flat metal steel strips welded at the edges. This greatly simplifies the laying of pipelines for various purposes.
8. in architecture
The huge dome made of synthetic film 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 operates in pneumatic container pipelines. The speed of the trains in them reaches 45 km/h. This type of transport is used for transporting bulk and other materials.
Container for transporting household waste.
YOU CAN DO THIS
1. Finish the phrase: “When a submarine dives, the air pressure in it.....”. Why?
2. Food for astronauts is prepared in semi-liquid form and placed in tubes with elastic walls. By lightly pressing on the tube, the astronaut removes the contents from it. What law is manifested in this?
3. What must be done to ensure that water flows through the tube from the vessel?
4. B oil industry To lift oil to the surface of the earth, compressed air is used, which is pumped by compressors into the space above the surface of the oil-bearing layer. What law is manifested in this? How?
5. Why does an empty paper bag, inflated with air, burst with a bang if you hit it with your hand or something hard?
6. Why do deep-sea fish have a swim bladder sticking out of their mouth when they are pulled to the surface?
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 water pressure decreases sharply and the air dissolved in the blood expands. The resulting bubbles clog blood vessels, interfering with blood flow, 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 of liquid to our mouth and “draw in” its contents. How? Why, in fact, does liquid rush into our mouth? The reason is this: when drinking, we expand the chest and thereby thin out 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 a 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, if you grab the neck of a bottle with your lips, you will not “draw” water from it into your mouth with any effort, since the air pressure in your mouth and above the water is the same. So, we drink not only with our mouths, but also with our lungs; after all, the expansion of the lungs is the reason that liquid rushes into our mouth.
Soap bubbles
“Blow a soap bubble,” wrote the great English scientist Kelvin, “and look at it: you can spend your whole life studying it, without ceasing to learn physics lessons from it.”
Soap bubble around a flower
Pour enough soap solution into a plate or tray so that the bottom of the plate is covered with a layer of 2 - 3 mm; A flower or 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 sufficient size, tilt the funnel, releasing the bubble from under it. Then the flower will be lying under a transparent semicircular cap made of soap film, shimmering with all the colors of the rainbow.
Several bubbles inside each other
A large soap bubble is blown from the funnel used for the described experiment. Then they completely immerse the straw in the soap solution so that only the tip, 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, without, however, bringing it to the edge, they blow out the second bubble contained in the first, in it - the third, fourth, etc. It is interesting to observe the bubble when it gets from a warm room into a cold one: it apparently decreases in volume and, conversely, swells when moving from a cold room to a warm one. The reason lies, of course, in the compression and expansion of the air contained inside the bubble. If, for example, in frosty weather at - 15° C, the volume of the bubble is 1000 cubic meters. cm and it comes from the cold 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 preserve a soap bubble for entire decades. The English physicist Dewar (famous for his work on air liquefaction) stored soap bubbles in special bottles, well protected from dust, drying out and air shock; under such conditions he managed to preserve some bubbles for a month or more. Lawrence in America managed to preserve soap bubbles under a glass cover for years.
Pascal's law - The pressure exerted on a liquid (gas) in any one place on its boundary, for example, by a piston, is transmitted without change to all points of the liquid (gas).
But it is usually used like this:
Let's talk a little about Pascal's Law:
Each particle of liquid located in the gravitational field of the Earth is affected by the force of gravity. Under the influence of this force, each layer of liquid presses on the layers below it. As a result, the pressure inside the liquid is at different levels there won't be the same. Therefore, in liquids there is pressure due to its weight.
From this we can conclude: The deeper we dive under water, the stronger the water pressure will act on us
The pressure due to the weight of the liquid is called hydrostatic pressure.
Graphically, the dependence of pressure on the depth of immersion in liquid is shown in the figure.
Based on Pascal's law Various hydraulic devices operate: brake systems, presses, pumps, pumps, etc.
Pascal's law not applicable in the case of a moving liquid (gas), as well as in the case when the liquid (gas) is in a gravitational field; Thus, it is known that atmospheric and hydrostatic pressure decreases with altitude.
In the Formula we used:
Pressure
Ambient pressure
Liquid density
Pascal's law
Corollary of Pascal's law
Pascal's law is formulated as follows:
It should be noted that in Pascal's law we're talking about not about pressures at different points, but about disturbances pressure, therefore the law is also valid for liquid in the field of gravity. In case moving incompressible fluid, we can conditionally speak of the validity of Pascal’s law, because adding an arbitrary constant value to the pressure does not change the form of the equation of motion of the fluid (the Euler equation or, if the action of viscosity is taken into account, the Navier–Stokes equation), but in this case the term Pascal's law as a rule not applied. For compressible liquids (gases), Pascal's law, generally speaking, is not valid.
Various hydraulic devices operate on the basis of Pascal’s law: brake systems, hydraulic presses, etc.
See also
Notes
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