Pascal law for liquids and gases Examples. Pascal law
This law was opened by the French scientist B. Pascal in 1653, it is sometimes called the basic law.
Pascal law can be explained from the point of view of the molecular structure of the substance. In solids, the molecule form a crystal lattice and fluctuate about their own. In liquids and gases, the molecules have relative freedom, they can move relative to each other. It is this feature that allows pressure produced on liquid (or gas) to transmit not only in the direction of force, but in all directions.
Pascal's law has been widely used in modern technique. On the law of Pascal, the work of modern superpress, which allow you to create pressure of about 800 MPa. Also on this law, the work of all hydroautomatics management was built. spacecraft, reactive airliners, numerical control machines, excavators, dump trucks, etc.
Hydrostatic fluid pressure
The hydrostatic pressure inside the liquid at any depth does not depend on the shape of the vessel in which the fluid is located, and equal to the product of the liquid, and the depth on which the pressure is determined:
In a homogeneous peopling pressure fluid at points lying in one horizontal plane (at one level), the same. In all cases shown in Fig. 1, fluid pressure on the bottom of the vessels is equally.
Fig.1. Independence of hydrostatic pressure from the form of a vessel
At this depth, the fluid presses the same in all directions, so the pressure on the wall at this depth will be the same as on the horizontal platform located at the same depth.
The total pressure in the liquid poured into the vessel is made of pressure from the surface of the liquid and hydrostatic pressure:
The pressure in the surface of the liquid is often equal to atmospheric pressure.
Examples of solving problems
Example 1.
| The task | In the hollow cube with an edge of 40 cm nanite water. Find the power of water pressure on the bottom and the walls of the cube. |
| Decision | Perform a picture.
1) hydrostatic pressure at depth The power of water pressure on the bottom of the Cuba: where is the bottom area; . 2) average pressure on side face Equally half ascemium at surface level and at the bottom level:
pressure force on the wall of the cube:
From the table density of water kg / m. We translate units into the system System: the length of the cube edge cm m. Calculate: 1) Pressure force on the bottom: 2) Pressure force on the wall: |
| Answer | Water pressure for the bottom and the walls of the cube 627 and 314 H respectively. |
Example 2.
| The task | In two knees of the U-shaped tube, water and oil separated by mercury are pillow. The surfaces of the mercury and liquids in both knees are at one height. Determine the height of the water column, if the height of the oil column is 20 cm. |
| Decision | Perform a picture.
According to the law of Pascal, the pressure in both knee tubes at the level is equally: Water pressure at level oil pressure at level Substitting the expressions for pressure fluids in the first equality, we get: |
(1623 - 1662)
Pascal law reads: "The pressure produced on liquid or gas is transmitted to any point of 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
In 1648, the fact that the pressure of the fluid depends on the height of its pillar, demonstrated splashes Pascal.
He put in a closed barrel, filled with water, a tube with a diameter of 1 cm2, a length of 5 m and, rising to the balcony of the second floor of the house, poured into this tube a water circle into this tube. When the water in it rose to the height of ~ 4 meters, the water pressure increased so much that the gaps were formed in a strong oak barrel, through which the water flowed.
Pascal tube
And now be attentive!
If you fill the same vessel size: one - liquid, the other - bulk material (for example, pea), to put a solid body close to the walls to the walls, to the surface of the substance in each vessel put the same circles, for example, from the wood / they should be seamless to the walls / , and on top set the same cargo by weight,
how does the pressure of the substance change on the bottom and the walls in each vessel? Think! In which case is the law of Pascal? How will the external pressure of goods be transmitted?
What technical devices are the law of Pascal?
Pascal law is based on the device of many mechanisms. See pictures, remember!
1. Hydraulic presses
The hydraulic multiplier is designed to increase the pressure (P2\u003e P1, since with the same pressure power S1\u003e S2).
Multipliers are used in hydraulic presses.
2. Hydraulic lifts
This is a simplified diagram of the hydraulic lift, which is installed on the dump trucks.
The purpose of the movable cylinder is an increase in the height of the piston lifting. To lower the cargo, the crane opens.
The filling unit for the supply of tractors is flammable as follows: the compressor pumps the air into a hermetically closed tank with a flammable, which goes along the hose to the tractor tank.
4. Sprayers
In sprayers used to combat agricultural pests, the pressure of the air is injected into the nucleus solution - 500,000 N / m2. The liquid is sprayed when the crane is open
5. Water supply systems
Pneumatic water system. The pump is supplied to the tank water compressing the airbag, and turns off when the air pressure is reached 400 000 N / m2. Water in pipes rises into rooms. When the air pressure decreases, the pump is again turned on.
6. Waterings
A jet of water emitted by a waterman under pressure of 1,000,000,000 n / m2, pierces the holes in metal dwarfs, crushes the breed in mines. Hydrophushki is equipped with modern fire fighting equipment.
7. When laying pipelines
Air pressure "sweels" pipes made in the form of flat metal steel tapes welded along the edges. This greatly simplifies the gasket of pipelines of various purposes.
8. In architecture
A huge dome of the synthetic film is maintained by pressure, a large atmospheric only at 13.6 n / m2.
9. Pneumatic pipelines
Pressure at 10,000 - 30 000 N / m2 works in pneumocontaine pipelines. The speed of the compositions in them reaches 45km / hour. This type of transport is used to transport bulk and other materials.
Container for the transport of household waste.
You can
1. Finished the phrase: "When immersing the submarine, air pressure in it .....". Why?
2. Food for astronauts produced in a semi-liquid form and placed in tubes with elastic walls. With a slight pressure on a tube, the cosmonaut extracts content from it. What law is manifested at the same time?
3. What needs to be done so that water flows out on the tube from the vessel?
4. In the oil industry for lifting oil to the surface of the Earth, a compressed air is used, which is injected with compressors into space above the surface of the oil-bearing layer. What law is manifested at the same time? How?
5. Why an empty paper bag, inflated by air, breaks down with a crash, if you hit your hand or something solid?
6. Why do deep-water fish when pulling them on the surface of the swimming bubble sticks out from the mouth?
BOOKSHELF
Do you know about it?
What is a caisson disease?
It manifests itself if it is very quickly rising from the depths of water. Water pressure sharply decreases and air dissolved in the blood expands. The resulting bubbles cloculate blood vessels, having a blood movement, and a person can perish. Therefore, scubars and divers float slowly so that the blood has time to determine the resulting air bubbles into the lungs.
How do we drink?
We put a glass or a spoon with a liquid to mouth and "pull" their contents. How? Why, in fact, the liquid rushes to us in the mouth? The reason is as follows: when drinking, we expand the chest and that we cut the air into the mouth; Under the pressure of the outer air, the liquid rushes into the space where the pressure is smaller, and thus penetrates into our mouth. Here is the same thing that would happen with liquid in the reporting vessels, if we cut the air over one of these vessels: under the pressure of the atmosphere, the liquid would have risen in this vessel. On the contrary, capturing the grooves of the Bottle, you do not "pull the water in her mouth with any efforts, since the pressure of the air in the mouth and above the water is equally. So, we drink not only mouth, but also light; After all, the expansion of the lungs is the reason that the fluid rushes into our mouth.
Bubble
"Plot a soap bubble," wrote the great English scientist Kelvin, "and look at him: you can study all my life by studying, without ceasing to extract physics lessons from it."
Soap bubble around flower
A soap solution is poured into a plate or a tray so that the bottom of the plate is covered with a layer of 2 - 3 mm; In the middle there is a flower or a vase and covered with a glass funnel. Then, slowly raising the funnel, blowing into its narrow tube, - a soap bubble is formed; When this bubble reaches sufficient sizes, tip the funnel, exciting a bubble from under it. Then the flower will be under a transparent semicircular cap from a soap film that transfers all the colors of the rainbow.
Several bubbles in each other
From a funnel used for the experiment described, a large soap bubble blows out. Then the straw in the soap solution is completely immersed so that only the tip of it, which will have to take into the mouth, remained dry, and hire it carefully through the first bubble wall to the center; Slowly pulling the straw back, without bringing it, however, to the edge, blow out the second bubble, enclosed in the first, in it - the third, fourth, etc. It is interesting to watch the bubble when it falls out of the warm premises in the cold: it apparently decreases In volume and, on the contrary, funerals, getting out of the cold room in warmth. The reason lies, of course, in compression and expansion of air enclosed inside the bubble. If, for example, in the frost in - 15 ° C, the volume of the bubble is 1000 cubic meters. See and he got into the room, where the temperature is + 15 ° C, it should increase in the amount of approximately 1000 * 30 * 1/273 \u003d about 110 cubic meters. cm.
The usual ideas about the short-life of soap bubbles are not quite correct: with proper appeal, it is possible to save a soap bubble in continuation of integer decades. English physicist Dewar (famous for its air liquefaction work) kept soap bubbles in special bottles, well protected from dust, drying and concussing air; Under such conditions, he managed to preserve some bubbles of the month or more. Lorenza in America managed to preserve soap bubbles under a glass cap.
The nature of fluid pressure, gas and solid is different. Although the pressure of the liquid and gas in various nature, their pressures have one identical effect that distinguishes them from solid. This effect, or rather the physical phenomenon, describes the law of Pascal.
Pascal law claims that the pressure produced by external forces into some place of fluid or gas is transmitted by fluid or gas without changing anywhere. This law was discovered with a brushing Pascal in the XVII century.
The law of Pascal means that if, for example, pressing gas with power in 10 H, 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), That pressure in the place of the application of 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 gas will increase on this magnitude. That is, the pressure will be transmitted unchanged to any point of gas.
The same is characteristic of liquids. But for solid bodies - no. This is due to the fact that the molecules of liquid and gas are movable, and in solids, although they can fluctuate, but remain in their place. In gases and liquids, the molecules move from a higher pressure region to the region with lower, so the pressure in the entire volume is quickly aligned.
Pascal's law is confirmed by experience. If in rubber ballfilled with water, pierce very small holes, then water will drip through them. If you press some one place of the ball now, then from all holes, regardless of how far they are from the place of the application of power, water is about the same in strength. This suggests that the pressure spread throughout the volume.
Pascal law finds practical use. If there is a certain force on a small surface area of \u200b\u200bthe liquid, then the increase in pressure will occur throughout the volume of the fluid. This pressure can be done to move the larger surface area.
For example, if on the area S 1 to turn the force of F 1, then the additional pressure P will be created throughout the volume:
This pressure is valid for F 2 to S 2:
From here it can be seen that the larger the area, the more power. That is, if we made a small force on the small area, then it turns into a greater force on a larger area. If the formula is replaced with pressure (P) on the initial force and the area, then this formula will be obtained:
F 2 \u003d (F 1 / S 1) * S 2 \u003d (F 1 * S 2) / s 1
We transfer F 1 to the left side:
F 2 / F 1 \u003d S 2 / S 1
It follows that F 2 is as many times more than F 1, how much s 2 more s 1.
Based on such a winnings, hydraulic presses are created. In them, a small force is applied to a narrow piston. As a result, in a wide piston there is a lot of force capable of raising a heavy load or put pressure on the pressed bodies.
Pressure in the liquid. Pascal law
In the liquids, the particles are movable, so they do not have their own form, but they have their own volume, resist compression and stretching; Do not resist shift deformations (fluidity property).
There are two types of static pressure in the resting liquid: hydrostatical and outdoor. Due to attraction to the ground, the fluid is putting pressure on the bottom and the walls of the vessel, as well as on the bodies inside it. The pressure due to the weight of the fluid column is called hydrostatic. The fluid pressure at different heights is different and does not depend on the orientation of the site to which it is produced.
Let the liquid be in a cylindrical vessel with a cross section of S; Liquid height H. Then
Hydrostatic fluid pressure depends on density r Fluids, from accelerating G free fall and from the depth H, on which the point under consideration is located. It does not depend on the form of a fluid column.
The depth H is counted vertically from the point under consideration to the level of the free surface of the fluid.
Under the conditions of weightless, the hydrostatic pressure in the liquid is absent, since in these conditions the fluid becomes weightless. The external pressure characterizes the compression of the fluid under the action of external force. It is equal:
An example of external pressure: atmospheric pressure and pressure generated in hydraulic systems. French scientist Blaze Pascal (1623-1662) installed: liquids and gases transmit pressure produced on them equally in all directions (Law Pascal). To measure pressures use manometers.
Their designs are very diverse. As an example, consider the device of the liquid pressure gauge. It is a U-shaped tube, one end of which is connected to the reservoir, in which the pressure is measured. By the difference in pillars in the knees of the pressure gauge, pressure can be determined.
No twos
It is known that gas fills the entire volume provided to him. At the same time, he presses on the bottom and walls of the vessel. This pressure is due to the movement and collision of gas molecules with the walls of the vessel. The pressure on all walls will be the same, since all directions are equal.
Gas pressure depends:
From the mass of gas - the more gas in the vessel, the greater the pressure,
- the volume of the vessel - the smaller the volume with the gas of a certain mass, the greater the pressure,
-The temperature - with increasing temperature, the speed of movement of molecules is increasing, which intensively interact and face the vessel walls, therefore the pressure increases.
For storage and transportation of gases, they are strongly compressed, their pressure is greatly increasing. Therefore, in such cases, special, very durable steel cylinders are used. In such cylinders, for example, preserve compressed air on submarines.
French physicist Blaze Pascal has established a law that describes the pressure of liquids or gases. Paskal's law: pressure acting on liquid or gas is transmitted unchanged into each point of liquid or gas.
In the liquid, as well as all the bodies on Earth, the power of gravity acts. Therefore, each layer of fluid, which is in the vessel, presses its weight to other layers, and this pressure, according to the law of Pascal, is transmitted in all directions. That is, inside the liquid there is pressure and at the same level it is the same in all directions. With a depth of pressure of the fluid increase. Also the pressure of the fluid depends on the properties of the fluid, i.e. From its density.
Since the fluid pressure increases with the depth, in the usual light safdra, the divers can work at a depth of up to 100 meters. At large depths require special protection. For a study at a depth of several kilometers, they use batisphere and bathyscaps that are withstanding considerable pressure.
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Pressure in the liquid. Pascal law. Dependence of pressure in fluid from depth
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In this lesson, we consider the difference between liquid and gaseous bodies from solids. If we want to change the volume of the fluid, we will have to apply a lot of effort comparable to the one we apply, changing the volume of the solid. Even to change the volume of gas, it is necessary to have a very serious effort, such as pumps and other mechanical devices. But if we want to change the shape of the liquid or gas and we will do it enough slowly, then we will not have any effort to apply. This is the main difference between fluid and gas from the solid.
Pressure in fluid
What is the reason for such an effect? The fact is that when displaced various layers of fluid relative to each other, it does not arise any forces associated with deformation. There are no shifts and deformations in liquid and gaseous media, in solid bodies when trying to move one layer against another significant forces of elasticity arise. Therefore, they say that the liquid seeks to fill the lower part of the volume in which it is placed. Gas seeks to fill the entire volume in which it is placed. But this is really a misconception, since if you look at our land from the side, we will see that gas (earthly atmosphere) is lowered down and seeks to fill some area on the ground surface. The upper boundary of this area is quite smooth and smooth, as well as the surface of the liquid, the filling sea, the oceans, the lake. The thing is that the gas density is significantly less than the density of the fluid, therefore, if the gas was very dense, he would definitely drop down and we saw the upper limit of the atmosphere. Due to the fact that in liquid and gas does not occur shifts and deformations - all forces interact between different areas of the liquid and gaseous medium, these are forces directed along the normal surface separating these parts. Such forces always aimed along the normal surface are called pressure forces. If we divide the pressure of the pressure on some surface to the area of \u200b\u200bthis surface, we obtain the pressure density, which is called simply pressure (or sometimes hydrostatic pressure is added), even in a gaseous medium, because from the point of view of pressure, the gaseous medium does not differ from liquid medium.
Pascal law
The properties of the distribution of pressure in liquid and gaseous media were studied from the beginning of the XVII century, the first who established the laws of the distribution of pressure in liquid and gaseous media was the French mathematician flashes Pascal.
The pressure value does not depend on the direction of normal to the surface on which it turns out this pressure is, that is, the pressure distribution is isotropically (equally) in all directions.
This law was established experimentally. Suppose that there is a rectangular prism in some liquid, one of the cathets of which is located vertically, and the second is horizontally. The pressure on the vertical wall will be equal to p 2, the pressure on the horizontal wall will be p 3, the pressure on the arbitrary wall will be p 1. Three sides form right triangleThe pressure forces acting on these parties are directed by normal to these surfaces. Since the dedicated volume is in a state of equilibrium, rest is not moving anywhere, therefore, the sum of the forces on it, equal to zero. The force acting on the normal to the hypotenuse is proportional to the surface area, that is, equal to the pressure multiplied by the surface area. Forces acting on the vertical and horizontal wall, are also proportional to the values \u200b\u200bof the areas of these surfaces and are also directed perpendicularly. That is, the force acting on the vertical is directed horizontally, and the force acting on the horizontal is directed vertically. These three strengths are equal to zero, therefore, they form a triangle, which is completely similar to this triangle.
Fig. 1. Distribution of forces acting on the subject
By virtue of the similarity of these triangles, and they are similar, since the sides forming them are perpendicular to each other, it follows that the proportionality coefficient between the areas of the sides of this triangle should be the same for all sides, that is, p 1 \u003d p 2 \u003d p 3.
Thus, we confirm the experimental law of Pascal, which argues that the pressure is directed in any direction and is equally large. So, we found that according to the law of Pascal, the pressure at this point of fluid is equally in all directions.
Now we prove that the pressure is at one level in the liquid everywhere equally.
Fig. 2. Forces acting on the walls of the cylinder
Imagine that we have a cylinder filled with a liquid with density ρ , the pressure on the walls of the cylinder, respectively, p 1 and p 2, since the mass of the liquid is at rest, the forces acting on the walls of the cylinder will be equal, since they are equal to them, that is, p 1 \u003d p 2. That's how we They proved that in the liquid at the same level the pressure is the same.
Dependence of pressure in fluid from depth
Consider the fluid located in the gravity field. The field of gravity acts on the liquid and tries to compress it, but the fluid is very weakly compressed, as it is not compressed and with any effect, the liquid density is always the same. This is a serious difference in gas fluid, so the formulas that we consider are related to incompressible fluid and are not applicable in the gas environment.
Fig. 3. Liquid object
Consider the object with the liquid S \u003d 1, height H, the liquid density ρ, which is in the field of gravity with the acceleration of the free fall g. From above, the pressure of the liquid P 0 and below the pressure P H, since the item is in the state of equilibrium, the sum of the forces on it will be zero. The strength of gravity will be equal to the density of the fluid to accelerate the free fall and on the volume of Ft \u003d ρ G V, since V \u003d H S, and S \u003d 1, then we will have FT \u003d ρ G H.
The total pressure force is equal to the pressure difference multiplied by the cross-sectional area, but since it is equal to us, then p \u003d p H - P 0
Since we do not move this item, then these two forces are equal to each other Ft \u003d P.
We obtain the dependence of the fluid pressure from depth or the law of hydrostatic pressure. The pressure at the depth H differs from the pressure on the zero depth by the value of ρ G H: p H \u003d p 0 + (ρ G H).
Law of reporting vessels
Using two concluded statements, we can bring another law - the law of reporting vessels.
Fig. 4. Reporting vessels
Two cylinders of different sections are interconnected, nallem liquid density ρ into these vessels. The law of reporting vessels claims: levels in these vessels will be absolutely the same. We prove this statement.
The pressure from above the smaller vessel P 0 will be less than the pressure at the bottom of the vessel at the value of ρ GH, the same pressure P 0 will be less pressure at the bottom and in a larger vessel on the same value of ρ GH, since they are the density and depth of them the same, therefore, These values \u200b\u200bwill have the same.
If you pour fluids into the vessels with different densities, then the levels will be different.
Conclusion. Hydraulic Press
The laws of hydrostatics were established by Pascal even at the beginning of the XVII century, and since then, on the basis of these laws, a huge number of various hydraulic machines and mechanisms work. We will look at the device that is called the hydraulic press.
Fig. 5. Hydraulic press
In a vessel, consisting of two cylinders, with a cross-section area S 1 and S 2, the liquid is installed at one height. Putting the pistons into these cylinders and putting the force F 1, we obtain f 1 \u003d p 0 s 1.
Due to the fact that the pressure attached to the pistons are the same, it is easy to see that the force you need to attach to a large piston to keep it alone will exceed the power that is applied to the small piston, the ratio of these forces has a large area Piston to share a small piston area.
Applying arbitrarily small effort to a small piston, we will develop a very large effort on a larger piston - it is in this way a hydraulic press works. The effort that will be applied to a greater press or to the part placed in the place will be highly large.
Next topic - Archimedes laws for fixed bodies.
Homework
- To define the law of Pascal.
- What approves the law of reporting vessels.
- Reply to site questions (source).
- Tikhomirova S.A., Yavorsky B.M. Physics ( a basic level of) - M.: Mnemozina, 2012.
- Gentendestein L.E., Dick Yu.I. Physics 10 class. - M.: Ilex, 2005.
- Gromov S.V., Rodina N.A. Physics Grade 7, 2002.
Pascal law for liquids and gases
The fluids and gases transmit pressure, which turns out to be on them, in all directions equally.
This law was opened in the middle of the XIV century by the French scientist B. Pascal and received his name later.
The fact that fluids and gases transmit pressure are explained by the large mobility of the particles from which they are composed, it significantly distinguishes them from solid, bodies whose particles are sediments, and can only make oscillations about the provisions of their equilibrium. Suppose gas, located in a closed vessel with a piston, its molecules evenly fill the entire volume provided to it. I will move the piston by reducing the volume of the vessel, the gas layer adjacent to the piston will be squeezed, the gas molecules will be placed more dense than at some distance from the piston. But after some time, the gas particles, participating in chaotic movement, are mixed with other particles, the gas density is leveled, but it will become more than before the movement of the piston. In this case, the number of blows of the bottom and the wall of the vessel increases, therefore, the pressure of the piston is transmitted to the gas in all directions the same and at each point increases on the same value. Similar arguments can be attributed to the fluid.
Formulation of the Law of Pascal
The pressure produced by external forces on the liquid (gas), which is in a state of rest is transmitted by the substance in all directions without a change to any point of the liquid (gas) and the walls of the vessel.
The Pascal law is performed for incompressible and compressible liquids and gases, if the compressibility is neglected. This law is a consequence of the law of conservation of energy.
Hydrostatic pressure of liquids and gases
Liquids and gases transmit not only external pressure, but also the pressure that occurs due to the existence of gravity. This force creates inside the liquid (gas) pressure, which depends on the depth of the immersion, while the applied external forces increase this pressure at any point of the substance to the same value.
Pressure that has a resting liquid (gas) is called hydrostatic. The hydrostatic pressure ($ p $) at any depth inside the liquid (gas) does not depend on the shape of the vessel in which it (it) is equal:
where $ h $ is the height of the fluid column (gas); $ \\ rho $ is the density of matter. From formula (1) for hydrostatic pressure, it follows that in all places of liquid (gas), which are at one depth, the pressure is the same. With increasing depth of hydrostatic pressure grows. So, at a depth of 10 km, the water pressure is approximately $ ^ 8pa $.
Corollary of the Law of Pascal: Pressure at any point on one horizontal level of fluid (gas), which is in a state of equilibrium has the same magnitude.
Examples of tasks with the solution
The task. There are three vessels of different shapes (Fig. 1). The bottom area of \u200b\u200beach vessel is $ s $. In which of the vessels the pressure of the same liquid on the bottom is the largest?
Decision. This task we are talking about a hydrostatic paradox. The consequence of the Law of Pascal is that the fluid pressure does not depend on the shape of the vessel, but determined by the height of the fluid column. Since, by the condition of the problem, the bottom area of \u200b\u200beach vessel is equal to S, from Fig. 1 we see that the height of the fluid pillars is the same, despite the various weight of the fluid, the power of the "weight" pressure on the bottom in all vessels is the same and equal to the weight of the fluid in the cylindrical vessel. The explanation of this paradox is that the power of the fluid pressure on the inclined walls has a vertical component, which is directed down into the tip of the vessel and pointing upward into the expanding.
The task. Figure 2 shows two communicating vessels with liquid. The cross section of one of the vessels in $ n \\ $ times less than the second. Vessels are closed with pistons. $ F_2 is applied to a small piston. \\ $ What power should be actuated on a large piston so that the system is in a state of equilibrium?
Decision. The task shows the scheme hydraulic presswhich works on the basis of the Law of Pascal. The pressure that creates the first piston on the liquid is:
The second piston has pressure on the fluid:
If the system is in equilibrium, $ p_1 $ and $ p_2 $ are equal to write:
We find a power module applied to a large piston:
Pressure in liquids Law Pascal
§ 11. Law of Pascal. Communicating vessels
Let fluid (or gas) be enclosed in a closed vessel (Fig. 17).
The pressure rendered to the liquid in any one place at its border, such as the piston, is transmitted unchanged to all liquid points - pascal law.
The law of Pascal is valid for both gases. This law can be derived, considering the conditions of equilibrium of arbitrary, mentally isolated in the liquid of cylindrical volumes (Fig. 17), taking into account the fact that the liquid presses on any surface only perpendicular to it.
Using the same technique, it can be shown that due to the presence of a homogeneous field of gravity, the pressure difference on two levels of liquid, stitching from each other at a distance `H`, is given by the ratio` deltap \u003d rhogh`, where` Rho` is the liquid density . this implies
in the reporting vessels filled with a homogeneous liquid, the pressure at all points of the liquid located in one horizontal plane is equally independent of the shape of the vessels.
In this case, the surface of the fluid in the reporting vessels is set at the same level (Fig. 18).
The pressure that appears in the liquid due to the gravity field is called hydrostatic. In the liquid at the depth of `H`, counting from the surface of the liquid, the hydrostatic pressure is equal to` p \u003d rhogh`. Full pressure in the fluid is made of pressure on the surface of the fluid (usually atmospheric pressure) and hydrostatic.
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Pascal law - The pressure rendered on the liquid (gas) in any one place at its border, for example, the piston, is transmitted unchanged in all points of liquid (gas).
But usually used like this:
Let's talk a little about the law of Pascal:
For each particle of fluid located in the field of land, the power of gravity acts. Under the action of this force, each layer of fluid presses the layers located under it. As a result, the pressure inside the liquid at different levels will not be same. Therefore, in fluids, there is a pressure due to its weight.
From this we can conclude: the deeper we will dive under water, the stronger the water pressure will be valid
The pressure due to the weight of the liquid is called hydrostatic pressure.
Graphically, the dependence of the pressure from the depth of immersion into the liquid is presented in the figure
Based law of Pascal Different hydraulic devices are working: brake systems, presses, pumps, pumps, etc.
Pascal law inapplicable in the case of a moving liquid (gas), as well as in the case when the liquid (gas) is in the gravitational field; So, it is known that atmospheric and hydrostatic pressure decreases with a height.
In the formula, we used:
Pressure
Pressure of the external environment
Liquid density
