Pressure refers to the pressure on the unit area of an objectpressure, the symbol isp（pressure）。Pressure is used to indicate the effect of pressure. The greater the pressure, the more obvious the effect of pressure.The calculation formula of pressure is:p=F/S, the unit of pressure isPascal(Par for short), the symbol is Pa.
The methods to increase the pressure are: increase the pressure when the force area is constant or reduce the force area when the pressure is constant.The methods to reduce the pressure are: reduce the pressure when the force area is constant or increase the force area when the pressure is constant.
The liquid has pressure on both the side wall and the bottom of the container, and the pressure increases with the increase of the liquid depth.
The characteristics of the internal pressure of the liquid are: the liquid has pressure from the inside to all directions;The pressure increases with the depth;At the same depth, the pressure of liquid in all directions is equal;The liquid pressure is also related to the density of the liquid. The greater the density of the liquid, the greater the pressure.The internal pressure of the liquid can bePiezometerTo measure.
Hydraulic jack, use a straw to suck drinks, stick the sucker on the smooth wall without falling off, use a needle to suck water, pull the cuppingPiston pump(According to the atmospheric pressure, the maximum capacity of the piston pump to pump water up to 10 meters can be calculated)navigation lock, water level indicator, return bend of sewer, etc.
cupping
Cupping, also known as "blood smearing therapy", is a kind of congestive therapy.It uses heat to exhaust the air in the tank, forming negative pressure, which quickly makes the tank tightly suck to the treatment site, causing congestion, thus producing therapeutic effect.This method is simple and effective.[3]
Hydraulic jack
The hydraulic jack applies the Pascal principle, that is, the pressure can be transferred from one object to another. For the incompressible static fluid, if the pressure at any point is increased by the external force, the pressure will be transmitted in all directions without change.Because "the greater the force area, the greater the pressure" under the condition that the pressure is constant, when pressing the handle of the hydraulic jack, the force area here is far smaller than the end where the weight is placed, and the area where the weight is placed will generate greater pressure, so the weight can be lifted.[4]
Piston pump
The main part of the piston pump is a pipe inserted into the water and a piston which can move up and down freely and contact with the pipe closely.Its working principle is to install a tight piston in a pipe, push the piston to the lower end of the pipe, and then insert the pipe into the water.When the piston is lifted, because there is no air under the piston, the atmospheric pressure acting on the water surface outside the pipe will force the water into the pipe, making the water rise with the piston.[5]
Intravenous infusion
Intravenous infusion is a method that a certain amount of sterile solution or liquid medicine is directly injected into the vein.The physical principle of intravenous infusion is that the internal pressure of the infusion system formed by atmospheric pressure and liquid venous pressure is higher than the human venous pressure.The sterile drug solution is input into the patient's vein through the needle tip through the infusion tube through the infusion bottle, and the following three conditions are required:
1. The infusion bottle must have a certain height to form sufficient water column pressure.The higher the height, the greater the water column pressure and the faster the drop velocity.
2. The liquid level in the infusion bottle must be connected to the atmosphere.As the liquid level is directly affected by atmospheric pressure, or the atmospheric pressure directly acts on the infusion soft bag, when the atmospheric pressure on the liquid level is higher than the human vein pressure, the liquid flows in the direction of low pressure.
3. The infusion pipeline must be kept unobstructed.The needle is not blocked, the infusion tube is not compressed and twisted, and the needle is in the vein.[6]
Connecter
The working principle of the connector is that the same kind of liquid that is still in the connector is always level with each liquid level that is in direct contact with the atmosphere.[7]
Change the pressure method
Methods of reducing pressure
one
When the pressure F is constant, the stress area S is increased;
two
When the force area S is constant, reduce the pressure F;
three
At the same time, reduce the pressure F and increase the force area S.[1]
Method of increasing pressure
one
When the pressure F is constant, reduce the force area S;
two
When the stress area S is constant, the pressure F increases;
three
At the same time, increase the pressure F and decrease the force area S.[1]
formula
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Definition formula:
Derivation process of liquid pressure formula:
Liquid pressure
To get the pressure somewhere under the liquid surface, we can imagine that there is a "plane" placed horizontally,The pressure of the liquid column above the plane on the plane is equal to the gravity of the liquid column.
The pressure of the liquid column above the plane on the planeF=G=mg=ρVg=ρShg，Pressure on the plane:
It represents the pressure law at the same temperature and mass
For the definition of pressure, four key points should be grasped:
⑴ When the stress area is fixed, the pressure increases with the increase of pressure.(At this time, the pressure is proportional to the pressure)
⑵ If the same pressure acts on the surface of the support, the pressure generated will be different if the force area is different.When the force area is small, the pressure is large;When the force area is large, the pressure is small.
⑶ Pressure and pressure are two completely different concepts: pressure is the force applied on the support surface and perpendicular to the support surface, independent of the area of the support surface and the size of the force area.
Pressure is the pressure on a unit area of an object, which is related to the force area and pressure.
⑷ The units of pressure and pressure are different.The unit of pressure isNewtonThe unit of force is the same as that of general force.The unit of pressure is a composite unit, which is composed of the unit of force and the unit of area.stayInternational System of UnitsThe middle is Newton/square meter, which is called“Pascal”, referred to as "Pa" for short.
③ Factors affecting the effect of pressure
1. When the force area is fixed, the greater the pressure, the greater the effect of pressure.
2. When the pressure is constant, the smaller the force area, the greater the effect of pressure.
(5) Physical meaning of 1Pa: the pressure on an area of 1 square meter is 1N.(A force of 1 N acts on one square meter)
1Pa size: the pressure of a flat newspaper on the horizontal table top, and the pressure of three sesame seeds on the horizontal table top is 1Pa.
Note: P=ρ gh can be used when the contact area between the uniform density cylinder and the contact surface is equal.
In the static liquid, take any liquid column whose bottom is a square (the square is parallel to the horizontal plane) and whose height is the depth for force analysis.The force acting on the liquid column is the gravity of the liquid column G=density * ghS, and the direction is vertical downward;The atmospheric pressure acting on the surface of the liquid column Fo=poS, in a vertical downward direction;The liquid pressure acting on the bottom of the liquid column, F=p * S, is vertically upward;The pressure on the four sides of the acting liquid column is horizontal, and the two are self balanced.There are downward gravity G, downward atmospheric pressure Fo and upward water pressure F acting on the vertical direction of the liquid column. Since the force is balanced in the vertical direction, F=Fo+G, that is
PS=poS+density * ghS. When S is removed, p=po+density * gh is obtained.If atmospheric pressure is not included, only the pressure generated by the liquid itself is counted, then p=ρ gh.
Company
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"P" refers to the pressure (note: it is a lowercase "p", not a capital "P", and the capital "P" refers to the workingpower），CompanyYes“Pascal”, referred to as "Pa", with the symbol "Pa".F is the force, and the unit is“Newton”, referred to as "cow", with the symbol of "N".S is the stress area, and the unit is“square meter”, the symbol is "㎡".
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The relationship between pressure, force and stress area is as follows:
Including:
P is the pressure
F stands for vertical force (pressure)
S represents the stress area
According to the above formula, the following formula can be derived: this formula is used for calculationliquidPressure, where:
G ≈ 9.8N/kg is the ratio of gravity and mass of the object (and is equal to the acceleration of gravity in numerical value) (sometimes for simple calculation or rough calculation, g can be taken as 10N/kg)
H meansVertical distance from a place below the liquid level to the free liquid level (the liquid level in contact with the atmosphere)[1]
Two formulas
project
pressure
formula
p=F/S
p=ρgh
Scope of application
General formula: cylindrical object
General liquid
General ideas
Horizontal plane: F=pS
First p=ρ gh, then p=F/S
Special ideas
Cylindrical object p=ρ gh
Liquid in regular container: F=G p=F/S
Measuring instrument
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Liquid column manometer
The common types of liquid column manometers are single tube manometers, inclined tube manometers, U-tube manometers, multiple manometers, etc. The common working liquids are water, mercury, etc.According to the hydrostatic principle, its working principle is to convert the measured pressure into the height of the liquid column for measurement.The pressure gauge is simple in structure and convenient in use. However, due to the low strength of the glass tube and the limitation of reading, it is generally used to measure low pressure or pressure difference.[2]
Load manometer
The common forms of load manometers are piston type, floating ball type and bell jar type manometers.According to the principle of liquid transmission pressure, its working principle is to convert the measured pressure into the mass of balance weight for measurement.Because both the piston and the weight can be accurately processed and measured, the pressure gauge has complex structure and high cost, but its measurement accuracy is high, and it is often used as a standard pressure measuring instrument to detect other types of pressure gauges.[2]
Elastic manometer
The common forms of elastic pressure gauge include membrane type, spring tube type, bellows type, etc.Its working principle is to use various forms of elastic elements to measure the deformation under pressure.The pressure gauge is characterized by simple structure, low price, firmness and durability, wide measurement range and sufficient measurement accuracy. It is a pressure measuring instrument widely used in industry.[2]
Electric manometer
Electric measuring pressure gauge is generally composed of measuring circuit, pressure transmitter and signal processor. Common pressure transmitters include strain gauge type, Hall gauge type, piezoresistive type, capacitive type, etc.According to the physical characteristics of metal or semiconductor, its working principle is to convert pressure into electrical signal for transmission and display for measurement.It is characterized by various forms, high measurement accuracy, wide measurement range, and long-distance signal transmission.In addition, it can work together with display instruments and measurement and control systems in the industrial production process to realize the measurement, automatic control and alarm of pressure and differential pressure.[2]
On May 8, 1654, a large number of people gathered around the experimental field in Madburg.Everyone has his own opinions. Some support Mayor Glick and hope that the experiment will be successful;Some assert that the experiment will fail;People are talking and arguing;Is predicting;Glick and his assistant put this in publicbrassA rubber band is padded in the middle of the hemispherical shell of the;Then fill the two hemispherical shells with water and join them;Then draw out all the water to formvacuum；Finally, tighten the faucet on the air nozzle and close it.At this time, the surrounding atmosphere tightly presses the two hemispheres together.With a wave of his hand, the four grooms led eight tall horses, tying four on each side of the ball.At Glick's command, the four grooms raised their whip to urge the horse and pulled away.
Experimental hemisphere
Four grooms and eight big horses were sweating all over.However, the copper ball was still intact, and Glick had to shake his hand to pause.Then, the left and right teams multiplied.The grooms drank some boiled water, wiped the sweat on their forehead, and were preparing for a second performance.Grick waved again, and the experimental field was even more lively.Sixteen big horses were pulling desperately, and eight horsemen were shouting and whipping their horses... The crowd who came to see the experiment stretched their necks and kept watching, making a "whoosh" sound from time to time.Suddenly, there was a loud bang, and the copper ball split into two original halves. Glick held up the two heavy hemispheres and proudly announced to everyone, "Ladies and gentlemen, you should believe it. There is atmospheric pressure, and the atmospheric pressure is so great, so shocking..." After the experiment, some people still did not understand why the two hemispheres could not be pulled apart,When he asked him, he patiently gave a detailed explanation: "At ordinary times, we close the two hemispheres together, without force, they will separate. This is because there is atmospheric pressure inside and outside the ball; they cancel each other out. It seems that there is no atmospheric effect.Now, after I vacuum it, there is no outward atmospheric pressure inside the ball, only the atmosphere outside the ball tightly presses the two hemispheres... ".
Through this "large-scale experiment", people finally believe thatvacuum；yesatmosphere；Atmospheric pressure;Atmospheric pressureIt's amazing, but Mayor Glick spent 4000 yuan for this experimentpound。
Experimental significance: It is the first time to prove the existence of atmospheric pressure, which is very large.
PascalIn 1648, he performed a famous experiment: he used a closed bucket filled with water, inserted a slender pipe on the lid of the bucket, and filled the thin pipe with water from the balcony of the building.As a result, only one glass of water was used to fracture the bucket, and the water in the bucket flowed out of the crack.Because of the small volume of the thin pipe, the depth of a cup of water is also very large.
This is the famous Pascal barrel cracking experiment in history.Liquid in a container,The pressure on the bottom (or side wall) of the container is far greater than the gravity of the liquid itself, which is inconceivable to many people。
improvement
The experimental device is too high to be demonstrated in the classroom, which can inspire students to think: can all devices be reduced accordingly?The answer is no.Then ask: the pipe length has decreased,Liquid pressureIf it is reduced, the pressure of liquid on the barrel must be reduced;Although the barrel is shrunk, its pressure resistance is almost unchanged, so it is impossible for the barrel to crack. Can other objects be used to simulate the "cracked barrel"?Students will naturally think of using objects with low pressure resistance to replace them (such as thin plastic bags).The essence of liquid pressure is very easy to understand when comparing the different situations of plastic bags filled with water under the action of a glass of water and a tube of water of the same quality.
Take a large sample for demonstrating liquid pressure measurementJar(about 30cm in diameter and 40cm in height), tie and seal the pipe orifice of the side wall at the lower part of the bottle with rubber film, pour red water from the bottle orifice, and as the water level in the bottle rises, the rubber film of the side pipe gradually bulges out. It can be seen that the degree of film bulge is not very obvious even after filling with water.This shows that although there is a lot of heavy water in the bottle, the pressure on the side wall is not very high.Take another one 1m longTorricelliThe glass tube is inserted into the large bottle through a cork with a small hole, and the cork is tightly sealed.Ask a student to stand on a stool and pour the water in the beaker into the tube gradually with a funnel. When the red water in the glass tube rises more than 50 cm, the rubber film of the side tube of the large bottle bulges out sharply, which is vivid and obvious.
Because the pressure of the liquid is equal to the density, depth andGravitational accelerationThe product of constants.In this experiment, the density of water remains the same, but as the depth increases again and again, the pressure at the lower part becomes larger and larger, and its hydraulic pressure finally exceeds the upper limit that the barrel can withstand, and the barrel will crack.
Torricelli experiment
Pascal's "barrel cracking" experiment can well prove that the liquid pressure is related to the depth of the liquid, but not to the mass of the liquid.
Torricelli experiment
TorricelliHe was the first person in the world to measure atmospheric pressure.Torricelli experimentThe specific value of atmospheric pressure is measured.Fill a 1m long glass tube closed at one end with mercury, block the tube orifice, and then insert it upside down in the mercury tank (keep vertical). When the finger blocking the tube orifice is released, the mercury surface in the tube will drop a little and will not drop again. At this time, the height difference between the mercury surface inside and outside the tube is 760mm.
The 760mm high mercury column in the tube is due to the existence of atmospheric pressure.According to the characteristics of the liquid pressure, the pressure on the liquid surface in the mercury tank should be equal to the pressure at the same height below the 760mm mercury column in the glass tube.The pressure on the liquid surface of the mercury tank is atmospheric pressure. As the mercury column in the glass tube is under vacuum, it cannot withstandatmospheric pressureThe pressure in the tube can only be generated by 760mm high mercury column.Therefore, the atmospheric pressure is equal to the pressure generated by 760 mm high mercury.
Generally, the common units for gas pressure arePascal, mm mercury column (mm mercury column), cm mercury column (cm mercury column), standard atmospheric pressure, their symbols arePa、mmHg、cmHg、Atm。
Relevant interpretation
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definition
① Pressure is the unit of objectthe measure of areaThe physical quantity of the pressure on the.
② The standard atmospheric pressure is 1.013 × 10 ≮ Pa, and the value of atmospheric pressure is equivalent to about 76cm (760mm)MercuryThe pressure produced by the column is the size of atmospheric pressure.
Explore the factors that affect the effect of stress
Fig. 1 Experiment of factors affecting the effect of pressure
As shown in Figure 1, figure A in Figure 1 places the small table on the sponge;Figure B in Figure 1 places a weight on the table;The third figure in Figure 1 turns the small table upside down and puts a weight on it.Pay attention to the depth of the sponge being pressed during the three tests, which shows the effect of pressure.
[Experimental conclusion] The effect of pressure is not only related to the size of pressure, but also related to the force area.When the force area is the same, the greater the pressure, the more obvious the effect of pressure;When the pressure is the same, the smaller the force area, the more obvious the effect of pressure.[1]
The presence of atmospheric pressure
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Sucking drinks with straws uses atmospheric pressure in physics
[Example 1] Sucking drinks with straws
When you suck the straw forcefully, the pressure inside the straw decreases, and the drink is pressed into the straw under the effect of the external atmospheric pressure, so that you can drink the drink instead of the usual suction.
[Example 2] Sucker sticks to smooth wall without falling off
Under the effect of its own elasticity, the central part of the suction cup tends to bulge outward, but because the inner wall is closely connected with the wall, air cannot enter, so the suction cup will cling to the wall under the action of atmospheric pressure.
[Example 3] Use a needle to absorb water
When the needle tube is pulled, a vacuum chamber is formed inside the needle cylinder. There is no pressure. Under the action of atmospheric pressure, water will be pressed into the needle cylinder through the needle head.
[Example 4] Cupping
Heat expansion and cold contraction of gas: heat the gas in the tank to make it swell, and cold contraction after pressing the skin to reduce the internal gas pressure.The atmospheric pressure or the pressure inside the body is greater than the gas pressure in the tank, which will make it absorb the skin.
Atmospheric pressure
The air is subject to gravity and has fluidity, so there is pressure inside the air in all directions. This pressure is calledAtmospheric pressure。
influence factor
Pressure device
① Temperature: The higher the temperature, the stronger the movement of air molecules, and the greater the pressure. ②Density: the higher the density is, the greater the air mass per unit volume is, and the greater the pressure is.
③Altitude: The higher the altitude, the thinner the air, and the lower the atmospheric pressure.
P is pressure, V is pressureGasVolume, nAmount of substance, T meansAbsolute temperature, R meansGas constant。All gases have the same R value.If pressure, temperature and volume are all adoptedInternational unit(SI), R=8.314 Pa · m ³/mole·K。If the pressure is atmospheric pressure and the volume is liter, then R=0.0814 atmospheric pressure · liter/mole · K.R isconstant
Under known standard conditions, the volume of 1mol ideal gas is about 22.4L
Because n=m/M, ρ=m/v (n is the amount of matter, m is the mass of matter, and M is theMolar mass, numerically equal to the molecular weight of the substance, ρ -density）Therefore, the Clapeyron equation can also be written in the following two forms:
Molar mass ratio=molecular weight ratio=density ratio=relative density.If mA=mBThen MA=MB。
2. At the same T · p:
Volume ratio=inverse ratio of molar mass;The ratio of two gas substances=the inverse ratio of molar mass
The ratio of material quantity=the inverse ratio of gas density;The volume ratio of two gases=the inverse ratio of gas density.
3. At the same T · v:
Inverse ratio of molar mass: pressure ratio of two gases=inverse ratio of molecular weight of gas.
inference
1、 Inference of Avogadro's Law
utilizeAvogadro's lawAs well as the relationship between the amount of substance and the number of molecules, molar mass, the following useful inferences can be obtained:
(1) At the same temperature and pressure: ① V1: V2=n1: n2=N1: N2 ② ρ 1: ρ 2=M1: M2 ③ At the same mass: V1: V2=M2: M1
(2) At the same temperature and volume: ④ p1: p2=n1: n2=N1: N2 ⑤ At the same mass: p1: p2=M2: M1
(3) At the same temperature, pressure and volume: ⑥ρ 1: ρ 2=M1: M2=m1: m2
Please deduce the specific derivation process to help you remember.The reasoning process is briefly described as follows:
(1) At the same temperature and pressure, gases with the same volume contain the same number of molecules. Therefore, at the same temperature and pressure, the volume of gases is proportional to the number of molecules, that is, to the amount of their substances, that is, for any gas, V=kn;Therefore, V1: V2=n1: n2=N1: N2, and then according to n=m/M, there is formula ②;If the gas mass is the same again, there will be Formula ③.
(2) According to Avogadro's law:temperatureWhen the volume and the number of gas molecules are the same, the pressure is also the same, that is, at the same temperature and volumeGas pressure It is proportional to the number of molecules.Other derivations are the same as (1).
(3) Under the same temperature, pressure and volume, the amount of gas must be the same. According to n=m/M and ρ=m/V, there is formula ⑥.Of course, these conclusions are not only applicable to two gases, but also to many gases.
2、 Relative density
At the same temperature and pressure, the density ratio appearing in the above conclusion formula ② and formula ⑥ is called the relative density of gas D=ρ 1: ρ 2=M1: M2.
Attention: ①D is called the relative density of gas 1 relative to gas 2, and has no unit, such as oxygenhydrogenThe density of is 16.
Unit conversion
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1.1 atm=0.1MPa=100kPa=1bar=10m water column=14.5PSI=1kg/cm ² To facilitate memory, it can be simplified as follows:
stayneutron starThe formation condition of is that the energy density reaches the critical pressurepressureThe unit of is the same as the unit of energy bulk density.This relationship can be derived from statistical physics.
explain
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not a fewsubjectThe pressure is often called pressure, and the pressure is called total pressure.At this time, the pressure does not represent the force, but the force acting vertically on the unit area of the object.Therefore, the vectorization of force and contact surface is no longer considered, and the pressure is treated as a scalar.
Pressure and pressure
There is a certain limit to the pressure that any object can withstand. If the limit is exceeded, the object will be damaged.
Pressure test
When an object is deformed due to external or internal causes, mutualForce, UnitsectionThis force on is called pressure.
Generally speaking, forsolidUnder the action of external force, compressive (or tensile) deformation and shear deformation will occur.Therefore, it is necessary to accurately describe these deformations of a solid and the effect of three components of the force acting on its three mutually perpendicular planes.In this way, the stress F/A has nine different components corresponding to each component Fx, Fy, Fz acting on three mutually perpendicular planes Ax, Ay, Az, so strictly speaking, the stress is onetensor。
Because the fluid cannot produce shear, it does not existShear stress。So for staticfluid, no matter how the force acts, there is only a force perpendicular to the contact surface;Because of the fluidIsotropySo no matter how oriented these surfaces are, at the same point, the force acting on the unit area is the same.becauseIdeal fluidAt each point of the, F/A is a fixed value in all directions, so the directionality of the stress F/A does not exist. Sometimes, this stress is called pressure, and in middle school physics, it is called pressure.The pressure is ascalar。The application of the definition of pressure (pressure) is generally limited to problems related to fluids.
verticalThe pressure acting on the unit area of an object.If P is used for pressure, the unit isPascal(1 Pascal=1 N/m2) (1Pa=1 N/m ²)
Non vectorization
Since pressure is a kind of stress, it already shows that pressure is not a vector.This can be further explained as follows: take the panel ds containing any point O in the object, and any force F or dF acts on the panelnormaldirectionincluded angle。The pressure generated by force F on face element ds is the ratio Fy/ds of the normal component of F in ds to ds, and the component Fx in the direction parallel to ds is the shear strength (shear strength) of face element ds.Then take the panel ds' orthogonal to ds, including point O, and it is easy to see that FY/ds' is the shear strength and Fx/ds' is the pressure.This shows that the same force acts on the same point, and the effect is different due to the different orientations of the selected bin, that is, the pressure is related to the direction of the selected bin.Therefore, when studying the pressure, we should not only consider the direction of the force, but also determine the direction of the surface;Usually, the positive normal direction of the bin is taken as the direction of the face. In this way, the face is also a vector.
According to the formula F=pS, F is a vector, S (ds) is also a vector, and the direction of F is always the same as that of S, so p must not be a vector.Because if P is also a vector, then the pressure multiplied by P and S is not a vector, nor is it actually a scalar.Because the force and area determining the stress are vectors, each vector has three components.In elasticity, stress is a quantity with nine components determined by force and area, called tensor.Pressure is the simplest one among tensors. The concept and operation of tensors are beyond the scope of physics in middle school.
Liquid pressure
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The pressure at the bottom, inner wall and inside of a liquid container is called liquid pressure, or hydraulic pressure for short.
What is liquid pressure
1. The liquid pressure is caused by gravity.If the liquidweightlessnessThere will be no pressure at all.
2. Due to the fluidity of liquid, the pressure generated by it has the following characteristics
(1) In addition to producing pressure on the bottom of the container, the liquid also produces pressure on the side wall that "limits" its flow.The solid only produces pressure on its bearing surface, and the direction is always perpendicular to the bearing surface.
The liquid level in each container is the same when the liquid in the connector is not flowing
(2) There is pressure in all directions inside the liquid, and the pressure in all directions at the same depth is equal.
(3) The formula for calculating the liquid pressure is p=ρ gh.It can be seen that the size of the liquid pressure only depends on the type of liquid (i.e. density ρ) and depth h, and the liquid qualityvolumeThere is no direct relationship.
(4) The liquid in the closed container can transmit the pressure it receives to all directions according to the original size.
3. The pressure of the liquid at the bottom of the container is not necessarily equal to the gravity of the liquid.The bottom of the container is subjected to the pressure of liquid F=pS=ρ ghS, and "ρ gSh" is the gravity of this liquid column.Because the liquid may be inclined.Therefore, the pressure on the bottom of the container may be equal to, or greater than or less than the gravity of the liquid itself.
Principle of liquid pressure
Principle of liquid pressure（Pascal's law）Pascal discovered the basic law of liquid pressure transmission, which is the famous Pascal's law.be-allHydraulic machineryAll are designed according to Pascal's law, so Pascal is called the "father of hydraulic press".
A few hundred years ago, Pascal noticed some phenomena in life, such as the flat water hose without irrigation, which became cylindrical when connected to the tap and filled with water.If there are several eyes on the hose, water will spray out of the small eyes in all directions.The water is flowing forward. Why can you round the hose?
Through observation, Pascal designed the "Pascal ball" experiment. Pascal ball is a hollow ball with many holes on the wall, connected to a cylinder, and movablepistonPour water into the ball and cylinder, press the piston inward, and water will be ejected from each small hole, becoming a "multi hole water gun".
The experiment of Pascal ball proves that the liquid can transmit the pressure it receives in all directions. Through observation, it is found that the distance of water ejected from each hole is about the same, which means that the pressure received by each hole is the same.
Pascal obtained the famous Pascal's law through the "Pascal ball" experiment:airtightThe pressure of any part of the liquid must be transmitted from the liquid to all directions according to its original size.
We know that pressure is generated by the force on an object, and as long as one object has pressure on the surface of another object, there is pressure. Similarly, water is subject togravityThe action has pressure on the bottom of the container, so water has pressure on the bottom of the container.The liquid has fluidity and pressure on the vessel wall, so the liquid also has pressure on the vessel wall.
In junior high school, the principle of liquid pressure can be expressed as follows: "There is pressure in all directions inside the liquid, and the pressure increases with the increase of liquid depth. The pressure of the same liquid in all directions at the same depth is equal; for different liquids, the pressure generated at the same depth is related to the density of the liquid. The greater the density, the greater the pressure of the liquid."
Internal pressure of liquid
1、 Homogeneous liquid
1. There is pressure in all directions
2. At the same depth, the pressure is the same
3. The deeper the depth, the greater the pressure
2、 Different liquids
At the same depth, the greater the density, the greater the pressure
Formula: p=ρ gh, where g=9.8N/kg or g=10N/kg, h is in m, ρ is in kg/m ³, and pressure p is in Pa.
Formula derivation:
The pressure formula can be derived from the basic formula: p=F/S
p=F/S=G/S=mg/S=ρVg/S=ρShg/S=ρhg=ρghF=ρ liquid gh, h refers toVertical distance from a place below the liquid level to the free liquid level (the liquid level in contact with the atmosphere)。
The pressure inside the liquid is only related to the depth and density of the liquid, and has nothing to do with the mass, volume, gravity, shape, bottom area, etc. of the liquid.
Measurement of body pressure of liquid U-tube piezometer
The liquid pressure measuring instrument is called "U-tube manometer". Using the liquid pressure formula p=ρ hg, h is the height difference between the two liquid levels, the pressure generated by calculating the liquid level difference is equal to the internal pressure of the liquid.
Formula: F1/S1=F2/S2
The pressure of the liquid on the bottom of the container when the cylinder is not upright can be calculated with p=ρ gh instead of p=F/S;The pressure of the liquid on the bottom of the container when the cylinder is not upright can be calculated by F=pS=ρ ghS.Because students have many questions about this problem, the two formulas p=F/S and p=ρ gh are simply explained as follows: the formula of liquid pressure p=ρ gh can be derived from P=F/S, but this is derived on the premise that the liquid container is a regular and uniform cylindrical container,Therefore, the use condition of the formula p=F/S is only applicable to this cylindrical container (this is different from solids, and the pressure between solids can always be calculated with p=F/S).But the formula p=ρ gh is based on the characteristics of the liquid itself (fluidity,ConnecterPrinciplePascal's lawEtc.) can be extended to any shapecontainer, any connected liquid with uniform density can be used.In fact, the formula of internal pressure of liquid can be derived in a more general and general way rather than the formula p=F/S——Mass forceOfpotential functionIt is just beyond the syllabus of middle school.
Due to the fluidity and non extensibility of the liquid, there is noTensile stressAnd shear stress, onlyCompressive stress(i.e. pressure), take out a small hexahedron randomly from the static liquid, and the hexahedron is in theEquilibrium stateWhen the hexahedron is infinitely shrunk, its gravity can be ignored, and it can be concluded that the pressure acting on the same point in all directions is equal, that is, the pressure is only related to the position coordinates, but not to the orientation.P=f (x, y, z)levelUp, z isVertical DownCoordinates of.The pressure of liquid is determined byMass forceWhen the liquid is static to the earth, it is caused by gravity, and the liquid mass m=1Unit mass forceAt eachcoordinateThe components of are X=0, Y=0, Z=g. The differential relationship between the pressure inside the liquid and the mass force is dp=ρ (XdxYdy+Zdz)=ρ (0 * dx+0 * dy+gdz)=ρ gdz (it can be seen from this equation thatlevelThere is no pressure difference above, and the horizontal plane isIsobaric surface, that is, the front, rear, left and right pressures are equal, and the pressure changes only in the gravity direction).From the water surface z=0 to the water depth z=h, the integral above gives p=ρ gh.
At the same depth, the greater the density, the greater the pressure.
Internal pressure of liquid: p=ρ gh (where ρ represents liquid density, g represents gravitational acceleration, and h representsFrom somewhere below the liquid level to the free liquid level) (the vertical distance of the liquid level in contact with the atmosphere）
If the question does not clearly state how much g equals, apply g=9.8N/kg, and then there are basically brackets behind the question. The contents of the brackets are the values of g and ρ.
Formula derivation: the pressure formula can be derived from the basic formula: p=F/S
Since the pressure in all directions at the same depth inside the liquid is equal, the vertical downward pressure of the liquid is calculated, and the pressure in all directions at this depth is also known.This formula gives a quantitativeInternal pressure of liquidThe law of.
Depth meansVertical distance from a place below the liquid level to the free liquid level (the liquid level in contact with the atmosphere)The pressure of the liquid is related to the depth and density of the liquid, but not to the mass of the liquid.
The liquid pressure is caused by gravity and has fluidity.
Factors affecting liquid pressure: depth, liquid density (independent of container shape, liquid mass and volume).
Measuring of liquid pressureinstrumentIt is called U-tube piezometer. Using the liquid pressure formula p=ρ gh, the pressure generated by the liquid level difference is equal to the internal pressure of the liquid.
