Solution of homogeneous differential equations of the nth order. Higher order differential equations

In the seventeenth century, the fact that air has a certain weight became known and proven to humanity. The assumption of its pressure on various items was proven using a special device - a barometer. It will be discussed in this article.

A device that determines air pressure

First, let's give a definition. A barometer is a device for measuring a certain air pressure on objects. Its inventor was E. Torricelli. In 1644, the barometer was a tube containing mercury and a measuring scale. On the day when the barometer was tested, the mercury level was at 760 mm, which was the reason to consider the mark at this level to be normal pressure. Such instruments are still used by meteorological stations.

Two centuries later, after the invention of the mercury barometer, as a result of many studies, Lucien Vidy constructed a fundamentally new liquid-free type. Subsequently called the aneroid barometer. Throughout their existence, aneroids have gained great popularity among many users, because they are small in size, lightweight and accurate. Compared to mercury barometers, aneroids are completely safe to use.

Types of barometers

Mercury is a device that measures pressure. The principle of operation is the movement of mercury relative to the applied scale.

Liquid - a device with which the pressure level is measured by balancing the weight of a liquid column with atmospheric pressure.

Aneroid barometer - the principle of operation and display of indicators is based on the change in the size of a sealed metal box filled with rarefied air under the influence of atmospheric pressure on its surface.

Electronic is modern look device that converts linear indicators classical aneroid into an electronic signal. The signals processed by the microprocessor are displayed on the liquid crystal screen.

An aneroid barometer is the most common of the above instruments, due to its small size and the lack of liquid in the mechanism. Let's look at it in more detail.

The structure of the atmospheric barometer

  • Round silver-nickel plate.
  • Box with ribbed bases.
  • Transmission mechanism.
  • Return spring.
  • Index arrow.

Atmospheric barometer - operating principle

When assembled, the aneroid is a box with various mechanisms. When a certain amount of air is pumped out of it, this creates a strong vacuum in the return spring, the indicator needle and the transmission mechanism between them. Under the influence of pressure, the walls of the “pressure chamber” contract or increase in size, and the index arrow begins to move relative to measuring scale towards increasing or decreasing pressure, respectively. At rest, the needle will be at 760 mm.

Self-recording barometer

Used to record meteorological data regarding fluctuations in atmospheric pressure. In other words, this is an improved aneroid barometer, with the addition of a clock mechanism to the pressure chamber, an apparatus that holds graduated paper, and a drive needle that applies an ink line to the paper.

The depicted “drawing” on the paper of the device is called a barogram. During the operation of the barograph, in accordance with hourly indicators, the mechanism winds special paper on its base, along the surface of which an attached arrow with ink slides and marks the indicators of deviations in atmospheric pressure.

Indicators of pressure discrepancies are recorded continuously. For meteorologists this is the main documentary fact weather changes in the near future. Depending on the size of the drum, the duration of recording can range from several hours to one week. The special design allows you to take readings and monitor atmospheric indicators at any time.

Barometer on your phone - what is it?

Technologies do not stand still, and now measure atmospheric pressure possible using a mobile device. Many users of modern gadgets, faced with new feature, they are wondering - a barometer on the phone, what is it? A modern miniature weather station allows the phone user to constantly check electronically the level of atmospheric pressure. Having tracked pressure readings for certain time, you can find out whether a cyclone or anticyclone is approaching. These indicators will be useful for people with hypersensitivity to sudden changes in pressure.

The capabilities of a mobile device don’t stop there. Electronically, it shows altitude, geographic width and longitude, which in turn helps quick search device and determining its exact location. Thanks to GPS satellites the process is fast and accurate. Mobile barometer is an accurate altimeter. The accuracy of determining the user's location is reduced to a radius of 3 meters. These are the devices that climbers use in the mountains. But they have gained great popularity in the aviation sector.

Barometer built into the watch

Appeared relatively recently. Few people know what this device is for, and most are wondering - a barometer in a watch, what is it?

Let's try to figure it out. Barometer in certain types hours presented in electronic or mechanical form. Electronic view- is no different from supplying atmospheric pressure data and displaying it on the screen, like on a phone. A watch with a mechanical pressure display is a perfectly accurate mini-copy of an aneroid. The only difference is in the simplified display scale. The cost of barometer watches is quite high, but, as a rule, they are shockproof and waterproof.

"Non-standard barometer"

Thanks to its founders it is called Harvard. The economic barometer underlies the formation of econometrics. Predicts changes in market conditions, dynamics of supply and demand, etc. Harvard Barometer is a description empirical patterns and extrapolations beyond recent months observations. They are based on a study of the dynamics of development of various economic indicators.

The development forecast was displayed graphically. Each curved line plotted on the graph displayed one or another indicator. For example, curve “A” displayed changes in average exchange rates (stock market); curve “B” displayed the index of wholesale prices and changes in trade turnover (production); curve “C” - reflected the rise or fall in the price of securities on the money market. IN perfect condition graphics - indicators “A” and “C” must coincide at the level of the maximum of the first unit and the minimum of the curve of the second unit.

Thanks to the leadership of W. Persons and W. Mitchell, the United States used this type of device until 1925. The Harvard Mitchell Barometer is the first powerful regulator and indicator of factors in national economy countries. Given the popularity and effectiveness of such construction and display of facts, this method has been adopted by many countries around the world. to the globe. But the prospect of development of many countries according to this ratio of indicators in the economy did not last long, because before and after the Second World War - in percentage terms they became irrelevant. The economies of all the countries that took part in the war were in complete decline, and to solve the problem of getting up from their knees, each country used its own methods to stabilize its own monetary currency. The old methods of raising indicators (getting out of the crisis) were not used at all, but the foundations laid by Mitchell became a precedent for the world economy.

Pressure gauge

It is worth noting another device that also measures pressure, not of air, but of gases and liquids - this device is called a pressure gauge. These two devices are very interconnected. The sum of the readings of the manometer and barometer is the absolute pressure, which has higher rate than atmospheric.

Conclusion

IN modern world A barometer is one of the main instruments of meteorology. The marked indicators on paper help many people learn about upcoming changes in atmospheric pressure and, accordingly, prepare for them. This is in to a greater extent applies to hypertensive patients. A barometer is an optional item in the home, but it is desirable as an auxiliary element or in addition to the interior. The modern frame of this much-needed device allows it to fit into any interior design.

The barometer, a device that measures air pressure on surrounding objects, was invented in the 17th century by the outstanding Italian scientist E. Torricelli. It originally looked like a glass tube with markings, filled with mercury inside. At the time of the study, the mercury column was at 760 mm; now this indicator is considered to be the level of normal pressure, by which it is judged whether the pressure increases or, on the contrary, decreases. This type of device thanks to high degree accuracy and are now used at various weather stations and in scientific laboratories.

After 2 centuries, having spent huge amount tests and using the developments of the outstanding German scientist Jacob Leibniz, engineer-inventor from France Lucien Vidy showed the world his “brainchild” - an improved aneroid barometer (from the Greek “aneros” - “without moisture”), which was much safer to use and had more light weight.

Today there are the following varieties:

  • Liquid barometers;
  • Mercury;
  • Aneroid barometers;
  • Electronic.

How the barometer works

Externally, a liquid barometer has the appearance of glass tubes interacting with each other like communicating vessels in accordance with hydrostatic laws. They are filled with mercury or other light-weight liquids (glycerin, oil).

Cup barometer

Cup - a glass tube with a closed end and a cup; pressure readings are determined by measuring the height of the liquid column, which starts from the level of the cup and ends at the mark of the upper meniscus.

Siphon barometer

Siphon - a tube with a closed long end, siphon-cup - two tubes, one open, the other closed + a cup, in them the air pressure readings are determined by determining the difference in the levels of the liquid column in the first and second tube.

Mercury barometer

A mercury barometer is a pair of communicating vessels, there is mercury inside, the top of one glass tube, about 90 cm long, is closed, there is no air there. Depending on changes in pressure, mercury rises or falls under the influence of air in a glass tube, and a small float shows the movement of the mercury mass and stops at a mark indicating its level in millimeters. The norm is mercury at 760 mm Hg. Art., readings above this value indicate a process of increasing pressure, below - a decrease. Barometers of this type are practically not used in everyday life, because mercury is dangerous toxic substance, the design of the barometer is quite cumbersome and requires careful handling. Therefore, they are widely used only in laboratory conditions, at various scientific meteorological stations and in industry, where absolute accuracy of data transmission is important.

Classic aneroid barometer

(1 - body; 2 - corrugated hollow metal box; 3 - glass; 4 - scale; 5- metal flat spring; 6 - spiral spring; 7 - thread; 8 - transmission mechanism; 9 - pointer arrow)

The operating system of a mechanical aneroid barometer, which does not contain any liquid, is based on the principle of air pressure acting on metal. In the middle of the device there is a box with thin corrugated metal walls, under the force of air the walls are compressed or unclenched, the lever turns the arrow in one direction or another. There are wall-mounted and table-top types, they are very convenient and practical to use, so they are very often used at home, in offices and various institutions.

Electronic barometer

An electronic (or digital) barometer is a modern version of this device; the linear indicators of a conventional aneroid barometer are converted into an electronic signal, which is processed by a microprocessor and displayed on a liquid crystal screen. It is compact in size, simple and easy to use, for example, for fishing, tourism or as a summer cottage option.

On at the moment there is already a digital version of barometers that are built in as additional function V mobile device or in barometer watches.

Observations of changes in atmospheric pressure are usually made using a mercury barometer. The principle of its device can be briefly described as follows: A glass tube about 90 cm long with one closed and one open end is completely filled with mercury. The open end of the tube is lowered into a small open vessel partially filled with mercury. Before immersion in the vessel, to prevent the mercury from leaking out, the end of the tube is closed with at least a finger. When the finger is removed, the mercury level in the tube will drop slightly and settle at a height of about 76 cm.

Mercury barometer

A void will form above the mercury in the tube and hence no pressure will be felt inside the tube above the mercury. Since atmospheric pressure acts on the free surface of the mercury in the vessel, it is obvious that the weight of the mercury column is above free surface it in the cup is balanced by the weight of the column of air above it, i.e. it should be equal to weight of this column of air Therefore, the length of the column of mercury in the tube at any moment indicates the pressure of the atmosphere. It is measured using a centimeter scale placed along a glass tube.

A direct reading from the barometer gives the length of the mercury column, the weight of which balances the weight of the air column above the barometer. The length of the mercury column also depends on the temperature that the barometer currently has. In order to make observations from different stations comparable to each other, a correction is introduced into the barometer readings for the thermal expansion of the tube, mercury and scale, with 0° C being considered the standard temperature.

The weight of a column of mercury also depends on the force of gravity in this place. Therefore, a second correction is introduced into the barometer readings. The value thus corrected corresponds to the pressure that would be observed at the station, with a gravity force equal to normal strength gravity at latitude 45° N.

Even with the most careful manufacture of barometers, small inaccuracies cannot be avoided, and barometer readings should therefore be corrected, taking into account individual errors of the device. When the barometer reading is corrected by instrumental correction, correction for thermal expansion and local gravity, we obtain the true pressure at the level of the cup of mercury.

In addition, it must be taken into account that atmospheric pressure decreases rapidly with altitude. Therefore, to compare the results of observations from different stations, it is also necessary to introduce a correction that brings the pressure at the altitude of a given station to the pressure at sea level. After making all the above corrections, the pressure value reported by each meteorological station corresponds to the pressure that would be observed by an accurate barometer placed at sea level, at 0 ° C, and a gravity equal to normal gravity at a latitude of 45 ° N.



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