EntrancePascal's law and its application. The practical significance of Pascal's law Blaise Pascal's main discoveries
Pascal's law can be formulated as follows: external pressure applied to a fluid at rest is transmitted to all its points without changes. This position follows from the basic equation of hydrostatics, from which it follows that external pressure applied to the boundary surface of a liquid is transmitted to all its points equally. In this case, external pressure can be applied to the liquid by means of gas, liquid and solid pressure on it.
Since all particles of a fluid at rest have the same hydrostatic head, then for any two of its points, in accordance with dependence (2.59), we can write
, (2.66)
where and are the geometric heights of the points under consideration relative to any comparison plane, and are the hydrostatic pressures at these points.
Based on relationship (2.66), Pascal’s law can be represented by the equation
from which it follows that any change in pressure at one point by an amount will cause exactly the same change in pressure at other points by the same amount, i.e.
The operation of many hydraulic machines that are widely used in technology is based on the application of Pascal's law. Such machines, in particular, include hydraulic presses, lifts and other similar hydraulic devices that make up the group of hydrostatic hydraulic machines.
The diagram of the hydraulic press is shown in Fig. 2.13. 
A relatively small external force applied to a small piston with a cross-sectional area creates a hydrostatic pressure equal to
The hydrostatic pressure at the level under another piston with a much larger area is determined according to Pascal's law by the equation
The difference in pressure is equal to
caused by the difference in geometric heights, compared to the high values of the pressures themselves in hydraulic presses and similar hydraulic devices, is insignificant and is usually not taken into account in calculations.
. (2.73)
Therefore, the force is as many times greater than the force as the area is greater than the area.
Due to some energy consumption during the pressing process to overcome friction in the piston seals and to overcome hydraulic resistance in the connecting pipelines, the actual pressing force will be slightly less than the force calculated by formula (2.73). Its value is determined from the expression
, (2.74)
where is the efficiency of the hydraulic press.
Liquid injection into hydraulic presses is usually carried out using special high-pressure pumps. As a rule, various technical oils are used as working fluids.
In most cases, hydraulic presses in industrial settings are used in combination with hydraulic accumulators.
The hydraulic accumulator (Fig. 2.14) is a device consisting of a cylinder and a massive piston, weighted with an additional load with a total weight of . The liquid pumped by the pump during the idling period of the press enters the accumulator, lifts the piston along with the load and accumulates in volume. During the power stroke, liquid 
will be pumped into the press simultaneously by both a pump and an accumulator. Thanks to this, the productivity of the press increases and continuous operation of the pump is ensured.
Rice. 2.14 noah productivity and pressure,
Blaise Pascal was a French mathematician, physicist and philosopher who lived in the mid-seventeenth century. He studied the behavior of liquids and gases and 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 the pressure exerted on them equally in all directions.
This principle is called Pascal's law for liquids and gases.
It is necessary to understand that this law did not take into account the force of gravity acting on the liquid. In reality, fluid pressure increases with depth due to gravity towards the Earth, and this is hydrostatic pressure.
To calculate its value, use the formula:
- pressure of the liquid column.
- ρ - liquid density;
- g - free fall acceleration;
- h - depth (height of the liquid column).
The total fluid pressure at any depth is the sum of hydrostatic pressure and pressure associated with external compression:
where p0 is the external pressure, for example, of a piston in a vessel 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 with a gain in force. Hydraulic devices are used to crush solids in presses. Aircraft have hydraulics 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.
Archimedes' power. Condition of floating bodies
Knowing Archimedean force (also known as buoyant force) is important when trying to understand why some bodies float while other bodies sink.
Let's look at an example. A man is in the pool. When he is completely submerged under water, he can easily perform a somersault, somersault, or jump very high. On land, performing such stunts is much more difficult.
This situation in the pool is possible due to the fact that the Archimedean force acts on a person in the water. In a liquid, pressure increases with depth (this is also true for gas). When the body is completely under water, the pressure of the liquid from below the body prevails over the pressure from above, and the body begins to float.
Archimedes' Law
A body in a liquid (gas) is subject to 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;
- ρl - density of liquid or gas;
- Vv. and. - the volume of displaced liquid (gas) equal to the volume of the immersed part of the body;
- Pv. and. - weight of displaced liquid.
Sailing condition
- FT>FA - the body is drowning;
- FT< FA - тело поднимается к поверхности до тех пор, пока не окажется в положении равновесия и не начнёт плыть;
- FT = FA - the body is in equilibrium in an aqueous or gaseous environment (floats).
Attention! The site administration is not responsible for the content of methodological developments, as well as for the compliance of the development with the Federal State Educational Standard.
- Participant: Kolesnikov Maxim Igorevich
- Head: Shcherbinina Galina Gennadievna
Introduction
Pascal's law became known in 1663. It was this discovery that formed the basis for the creation of superpresses with a pressure of over 750,000 kPa, a hydraulic drive, which in turn led to the emergence of hydraulic automation that controls modern jetliners, spaceships, numerically controlled machines, powerful dump trucks, mining combines, presses, and excavators. .. Thus, Pascal's law has found great application in the modern world. However, all these mechanisms are quite complex and cumbersome, so I wanted to create devices based on Pascal’s law in order to convince myself and convince my classmates, many of whom believe that it is stupid to waste time on “antiquity” when we are surrounded by modern devices that this topic is still interesting and relevant. In addition, devices created by oneself, as a rule, arouse interest, make one think, fantasize, and even look at the discoveries of “deep antiquity” with different eyes.
Object My research is Pascal's law.
Goal of the work: experimental confirmation of Pascal's law.
Hypothesis: knowledge of Pascal's law can be useful for designing construction equipment.
Practical significance of the work: My work presents experiments for demonstration in physics lessons in the 7th grade of a secondary school. The developed experiments can be demonstrated both in class when studying phenomena (I hope that this will help form some concepts when studying physics), and as homework for students.
The proposed installations are universal; one installation can be used to demonstrate several experiments.
Chapter 1. All our dignity is in the ability to think
Blaise Pascal (1623-1662) – French mathematician, mechanic, physicist, writer and philosopher. A classic of French literature, one of the founders of mathematical analysis, probability theory and projective geometry, creator of the first examples of computing technology, author of the basic law of hydrostatics. Pascal entered the history of physics by establishing the fundamental law of hydrostatics and confirmed Toricelli’s assumption about the existence of atmospheric pressure. The SI unit of pressure is named after Pascal. Pascal's law states that the pressure exerted on a liquid or gas is transmitted to any point without change in all directions. Even the famous Archimedes' law is a special case of Pascal's law.
Pascal's law can be explained using the properties of liquids and gases, namely: molecules of liquid and gas, hitting the walls of a container, create pressure. Pressure increases (decreases) with increasing (decreasing) concentration of molecules.
There is a widespread problem that can be used to understand the operation of Pascal's law: when fired from a rifle, a hole is formed in a boiled egg, since the pressure in this egg is transmitted only in the direction of its movement. A raw egg breaks into pieces, since the pressure of a bullet in a liquid, according to Pascal's law, is transmitted equally in all directions.
By the way, it is known that Pascal himself, using the law he discovered, in the course of his experiments, invented a syringe and a hydraulic press.
Practical significance of Pascal's law
The operation of many mechanisms is based on Pascal's law; otherwise, such properties of gas as compressibility and the ability to transmit pressure equally in all directions have found wide application in the design of various technical devices.
- Thus, compressed air is used in a submarine to lift it from depth. When diving, special tanks inside the submarine are filled with water. The weight of the boat increases and it sinks. To lift the boat, compressed air is pumped into these tanks, which displaces the water. The weight of the boat decreases and it floats up.
Fig.1. Submarine on the surface: the main ballast tanks (CBT) are not filled
Fig.2. Submarine in a submerged position: the Central City Hospital was filled with water
- Devices that use compressed air are called pneumatic. These include, for example, a jackhammer, which is used to open asphalt, loosen frozen soil, and crush rocks. Under the influence of compressed air, the peak of a jackhammer makes 1000-1500 blows per minute of great destructive force.
- In production, a pneumatic hammer and a pneumatic press are used for forging and processing metals.
- Air brakes are used in trucks and railway vehicles. In subway cars, doors are opened and closed using compressed air. The use of air systems in transport is due to the fact that even if air leaks from the system, it will be replenished due to the operation of the compressor and the system will function properly.
- The operation of an excavator is also based on Pascal's law, where hydraulic cylinders are used to drive its booms and bucket.
Chapter 2. The soul of science is the practical application of its discoveries
Experiment 1 (video, method of modeling the operating principle of this device at the presentation)
The action of Pascal's law can be observed in the operation of a laboratory hydraulic press, consisting of two connected left and right cylinders, uniformly filled with liquid (water). The plugs (weights) indicating the fluid level in these cylinders are highlighted in black.
Rice. 3 Diagram of a hydraulic press
Rice. 4. Application of hydraulic press
What happened here? We pressed down on the plug in the left cylinder, which forced the fluid out of this cylinder towards the right cylinder, as a result of which the plug in the right cylinder, experiencing fluid pressure from below, rose. Thus, the fluid transmitted pressure.
I conducted the same experiment, only in a slightly different form, at home: a demonstration of an experiment with two cylinders connected to each other - medical syringes connected to each other and filled with liquid-water.
The design and operating principle of a hydraulic press is described in a 7th grade textbook for secondary schools,
Experiment 2 (video, using the modeling method to demonstrate the assembly of this device at a presentation)
In development of the previous experiment, to demonstrate Pascal’s law, I also assembled a model of a wooden mini-excavator, the basis of which is piston cylinders filled with water. Interestingly, as pistons that raise and lower the boom and bucket of the excavator, I used medical syringes invented by Blaise Pascal himself to confirm his law.
So, the system consists of ordinary medical syringes of 20 ml (function of control levers) and the same syringes of 5 ml (function of pistons). I filled these syringes with liquid - water. A dropper system was used to connect the syringes (provides sealing).
In order for this system to work, we press the lever in one place, the water pressure is transmitted to the piston, to the plug, the plug rises - the excavator begins to move, the excavator boom and bucket are lowered and raised.
This experiment can be demonstrated by answering the question after § 36, page 87 of A.V. Peryshkin’s textbook for 7th grade: “What experience can be used to show the peculiarity of the transmission of pressure by liquids and gases?” The experiment is also interesting from the point of view of the availability of the materials used and practical application of Pascal's law.
Experience 3 (video)
Let's attach a hollow ball (pipette) with many small holes to the tube with a piston (syringe).
Fill the balloon with water and press the plunger. The pressure in the tube will increase, water will begin to pour out through all the holes, and the water pressure in all streams of water will be the same.
The same result can be obtained if you use smoke instead of water.
This experiment is a classic demonstration of Pascal's law, but the use of materials available to each student makes it especially effective and memorable.
A similar experience is described and commented on in a 7th grade textbook for secondary schools,
Conclusion
In preparation for the competition, I:
- studied theoretical material on the topic I chose;
- created home-made devices and conducted an experimental test of Pascal's law on the following models: a model of a hydraulic press, a model of an excavator.
conclusions
Pascal's law, discovered in the 17th century, is relevant and widely used in our time in the design of technical devices and mechanisms that facilitate human work.
I hope that the installations I have collected will be of interest to my friends and classmates and will help me better understand the laws of physics.
What the French physicist and mathematician, polemicist and writer invented, you will learn from this article.
Blaise Pascal discoveries, inventions, achievements
Blaise Pascal's contributions to computer science
The future inventor was born into the family of a famous mathematician at that time. Therefore, he did not go to school, and his father replaced his teachers. He instilled in him a love of mathematics and from an early age the boy could perform complex calculations. At the age of 15, Pascal communicated with Parisian scientists as equals, discussing complex problems in mathematics. A year later, the young man conducted his first research, and it became clear that a brilliant future awaited him, and the world would see a new mathematical genius.
Blaise Pascal decided to make the work of his father, who held the post of royal and official, easier and decided to create an arithmetic machine. The meticulous work on the adding machine lasted for three whole years. Blaise Pascal's calculating machine glorified him throughout the world. A small brass box, which had a complex mechanism, was exhibited at the Luxembourg Palace. This invention became a kind of foundation for the creation of computer science, because his machine performed automatic calculations that a modern computer does today.
Blaise Pascal, whose invention was called the new wonder of the world, was already fascinated by a new topic - atmospheric pressure. The scientist was confident that weather conditions could be measured using a column of mercury in a glass tube. Thanks to this conclusion, he managed to discover the laws of fluid pressure.
After the death of his father and some events in his life, Pascal decided to enter a monastery. One day, while in his cell, he felt a terrible toothache. And in order to somehow distract himself from the pain, he began to think about the mathematical curve. Caught by an unknown inspiration, Pascal began to prove theorems one after another. He was the first one so close approached the creation of the foundations of higher mathematics, but, unfortunately, did not have time to do this.
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, describes Pascal's law.
Pascal's law The pressure produced by external forces at some point in a liquid or gas is transmitted through the liquid or gas without change to any point.
Pascal's law was discovered by the French scientist B. Pascal in 1653, this law is confirmed by various experiments.
Pressure is a physical quantity equal to the modulus of the force F acting perpendicular to the surface, which is per unit area S of this surface.
Pascal's law formula Pascal's law is described by the pressure formula:
\(p = \dfrac(F)(S)\)
where p is the pressure (Pa), F is the applied force (N), S is the surface area (m2).
Pressure is a scalar quantity It is important to understand that pressure is a scalar quantity, that is, it has no direction.
Ways to reduce and increase pressure:
In order to increase the pressure, it is necessary to increase the applied force and/or reduce the area of its application.
Conversely, to reduce pressure, it is necessary to reduce the applied force and/or increase the area of its application.
The following types of pressure are distinguished:
- atmospheric (barometric)
- absolute
- excess (gauge)
Gas pressure depends on:
- from the mass of gas - the more gas in the vessel, the greater the pressure;
- on the volume of the vessel - the smaller the volume with a gas of a certain mass, the greater the pressure;
- from temperature - with increasing temperature, the speed of movement of molecules increases, which interact more intensely and collide with the walls of the vessel, and therefore the pressure increases.
Liquids and gases transmit in all directions not only the pressure exerted on them, but also the pressure that exists inside them due to the weight of their own parts. The upper layers press on the middle ones, and the middle ones on the lower ones, and the lower ones on the bottom.
There is pressure inside the liquid. At the same level, it is the same in all directions. With depth, pressure increases.
Pascal's law means that if, for example, you press on a gas with a force of 10 N, and the area of this pressure is 10 cm2 (i.e. (0.1 * 0.1) m2 = 0.01 m2), then the pressure in the place where the force is applied will increase by p = F/S = 10 N / 0.01 m2 = 1000 Pa, and the pressure in all places of 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 of higher pressure to an area of lower pressure, so that the pressure throughout the volume quickly equalizes.
Unlike solids, liquids and gases in a state of equilibrium do not have elastic shape. They have only volumetric elasticity. In a state of equilibrium, the voltage in a liquid and gas is always normal to the area on which it acts. Tangential stresses cause only changes in the shape of elementary volumes of the body (shifts), but not the magnitude of the volumes themselves. For such deformations in liquids and gases, no effort is required, and therefore, in these media at equilibrium, tangential stresses do not arise.
law of communicating vessels in communicating vessels filled with a homogeneous liquid, the pressure at all points of the liquid located in the same horizontal plane is the same, regardless of the shape of the vessels.
In this case, the surfaces of the liquid in communicating vessels are installed at the same level
The pressure that appears in a liquid due to the gravitational field is called hydrostatic. In a liquid at a depth \(H\), counting from the surface of the liquid, the hydrostatic pressure is equal to \(p=\rho g H\) . The total pressure in a liquid is the sum of the pressure at the surface of the liquid (usually atmospheric pressure) and hydrostatic pressure.
Javascript is disabled in your browser.To perform calculations, you must enable ActiveX controls!