Okei is an all-Russian classifier of units of measurement. Measuring quantities Mm unit of measurement

This lesson will not be new for beginners. We have all heard from school such things as centimeter, meter, kilometer. And when it came to mass, they usually said gram, kilogram, ton.

Centimeters, meters and kilometers; grams, kilograms and tons have one common name - units physical quantities .

In this lesson we will look at the most popular units of measurement, but we will not delve too deeply into this topic, since units of measurement go into the field of physics. Today we are forced to study part of physics because we need it for further study of mathematics.

Units of length

The following units of measurement are used to measure length:

• millimeters;
• centimeters;
• decimeters;
• meters;
• kilometers.

millimeter(mm). Millimeters can even be seen with your own eyes if you take the ruler that we used at school every day

Small lines running one after another are millimeters. More precisely, the distance between these lines is one millimeter (1 mm):

centimeter(cm). On the ruler, each centimeter is marked with a number. For example, our ruler, which was in the first picture, had a length of 15 centimeters. The last centimeter on this ruler is marked with the number 15.

There are 10 millimeters in one centimeter. You can put an equal sign between one centimeter and ten millimeters, since they indicate the same length:

1 cm = 10 mm

You can see this for yourself if you count the number of millimeters in the previous figure. You will find that the number of millimeters (distances between lines) is 10.

The next unit of length is decimeter(dm). There are ten centimeters in one decimeter. An equal sign can be placed between one decimeter and ten centimeters, since they indicate the same length:

1 dm = 10 cm

You can verify this if you count the number of centimeters in the following figure:

You will find that the number of centimeters is 10.

The next unit of measurement is meter(m). There are ten decimeters in one meter. One can put an equal sign between one meter and ten decimeters, since they indicate the same length:

1 m = 10 dm

Unfortunately, the meter cannot be illustrated in the figure because it is quite large. If you want to see the meter live, take a tape measure. Everyone has it in their home. On a tape measure, one meter will be designated as 100 cm. This is because there are ten decimeters in one meter, and one hundred centimeters in ten decimeters:

1 m = 10 dm = 100 cm

100 is obtained by converting one meter to centimeters. This is a separate topic that we will look at a little later. For now, let's move on to the next unit of length, which is called the kilometer.

The kilometer is considered the largest unit of length. There are, of course, other higher units, such as megameter, gigameter, terameter, but we will not consider them, since a kilometer is enough for us to further study mathematics.

There are a thousand meters in one kilometer. You can put an equal sign between one kilometer and a thousand meters, since they indicate the same length:

1 km = 1000 m

Distances between cities and countries are measured in kilometers. For example, the distance from Moscow to St. Petersburg is about 714 kilometers.

International System of Units SI

The International System of Units SI is a certain set of generally accepted physical quantities.

The main purpose of the international system of SI units is to achieve agreements between countries.

We know that the languages ​​and traditions of the countries of the world are different. There's nothing to be done about it. But the laws of mathematics and physics work the same everywhere. If in one country “twice two is four,” then in another country “twice two is four.”

The main problem was that for each physical quantity there are several units of measurement. For example, we have now learned that to measure length there are millimeters, centimeters, decimeters, meters and kilometers. If several scientists speaking different languages ​​gather in one place to solve some problem, then such a large variety of units of length measurement can give rise to contradictions between these scientists.

One scientist will state that in their country length is measured in meters. The second may say that in their country the length is measured in kilometers. The third may offer his own unit of measurement.

Therefore, the international system of SI units was created. SI is an abbreviation for the French phrase Le Système International d’Unités, SI (which translated into Russian means the international system of units SI).

The SI lists the most popular physical quantities and each of them has its own generally accepted unit of measurement. For example, in all countries, when solving problems, it was agreed that length would be measured in meters. Therefore, when solving problems, if the length is given in another unit of measurement (for example, in kilometers), then it must be converted into meters. We'll talk about how to convert one unit of measurement to another a little later. For now, let's draw our international system of SI units.

Our drawing will be a table of physical quantities. We will include each studied physical quantity in our table and indicate the unit of measurement that is accepted in all countries. Now we have studied the units of length and learned that the SI system defines meters to measure length. So our table will look like this:

Mass units

Mass is a quantity indicating the amount of matter in a body. People call body weight weight. Usually when something is weighed they say “It weighs so many kilograms” , although we are not talking about weight, but about the mass of this body.

However, mass and weight are different concepts. Weight is the force with which the body acts on a horizontal support. Weight is measured in newtons. And mass is a quantity that shows the amount of matter in this body.

But there is nothing wrong with calling body weight weight. Even in medicine they say "person's weight" , although we are talking about the mass of a person. The main thing is to be aware that these are different concepts.

The following units of measurement are used to measure mass:

• milligrams;
• grams;
• kilograms;
• centners;
• tons.

The smallest unit of measurement is milligram(mg). You will most likely never use a milligram in practice. They are used by chemists and other scientists who work with small substances. It is enough for you to know that such a unit of measurement of mass exists.

The next unit of measurement is gram(G). It is customary to measure the amount of a particular product in grams when preparing a recipe.

There are a thousand milligrams in one gram. You can put an equal sign between one gram and a thousand milligrams, since they mean the same mass:

1 g = 1000 mg

The next unit of measurement is kilogram(kg). The kilogram is a generally accepted unit of measurement. It measures everything. The kilogram is included in the SI system. Let us also include one more physical quantity in our SI table. We will call it “mass”:

There are a thousand grams in one kilogram. You can put an equal sign between one kilogram and a thousand grams, since they denote the same mass:

1 kg = 1000 g

The next unit of measurement is hundredweight(ts). In centners it is convenient to measure the mass of a crop collected from a small area or the mass of some cargo.

There are one hundred kilograms in one centner. One can put an equal sign between one centner and one hundred kilograms, since they denote the same mass:

1 c = 100 kg

The next unit of measurement is ton(T). Large loads and masses of large bodies are usually measured in tons. For example, the mass of a spaceship or car.

There are one thousand kilograms in one ton. One can put an equal sign between one ton and a thousand kilograms, since they denote the same mass:

1 t = 1000 kg

Time units

There is no need to explain what time we think is. Everyone knows what time is and why it is needed. If we open the discussion to what time is and try to define it, we will begin to delve into philosophy, and we do not need this now. Let's start with the units of time.

The following units of measurement are used to measure time:

• seconds;
• minutes;
• watch;
• day.

The smallest unit of measurement is second(With). There are, of course, smaller units such as milliseconds, microseconds, nanoseconds, but we will not consider them, since this moment this makes no sense.

Various parameters are measured in seconds. For example, how many seconds does it take for an athlete to run 100 meters? The second is included in the SI international system of units for measuring time and is designated as "s". Let us also include one more physical quantity in our SI table. We will call it “time”:

minute(m). There are 60 seconds in one minute. One minute and sixty seconds can be equated because they represent the same time:

1 m = 60 s

The next unit of measurement is hour(h). There are 60 minutes in one hour. An equal sign can be placed between one hour and sixty minutes, since they represent the same time:

1 hour = 60 m

For example, if we studied this lesson for one hour and we are asked how much time we spent studying it, we can answer in two ways: “we studied the lesson for one hour” or so “we studied the lesson for sixty minutes” . In both cases, we will answer correctly.

The next unit of time is day. There are 24 hours in a day. You can put an equal sign between one day and twenty-four hours, since they mean the same time:

1 day = 24 hours

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IN modern world there are many units of measurement for various quantities. Not all of them are often used, but they all have a right to exist. Most often, the use of a particular unit of measurement depends on the location. For example, we are used to measuring length in millimeters, centimeters, meters, kilometers. However, when buying a foreign-made TV, we inevitably come across such a unit of length as an inch, because it is usually the diagonal length of a TV that is indicated in inches. Imagine, for example, you are buying a TV, as is now fashionable, through an online store. The website states that its diagonal is 24 inches. And here the problem arises: how much is 24 inches? And mathematics comes to the rescue. Another example: any student studying physics has heard about the SI system of units of measurement. Moreover, the modern curriculum requires every student to be able to convert units of measurement to the SI system when solving school problems in physics. There are many such examples. The point is that you need to be able to navigate the units of measurement of various quantities and, if necessary, be able to convert one unit of measurement to another.

We present the most common units of measurement of basic quantities.

Mass: milligram, gram, kilogram (SI), centner, ton.

1 ton = 10 quintals = 1,000 kg = 1,000,000 g = 1,000,000,000 mg.

Length: millimeter, centimeter, meter (SI), kilometer, foot, inchm.

1 km = 1,000 m = 100,000 cm = 1,000,000 mm

1 m = 3.2808399 feet = 39.3707 inches

Area: cm2, m2 (SI), acre, foot2, hectare, in2.

1 m 2 = 10,000 cm 2 = 0.00024711 acres = 10.764 feet = 0.0001 hectares = 1,550 inches 2.

Volume: 3 centimeter, 3 meter (SI), 3 foot, gallon, 3 inch, liter.

1 m 3 = 1,000,000 cm 3 = 35.32 ft 3 = 220 gallons = 61,024 in 3 = 1,000 liters (dm 3).

As a rule, schoolchildren do not have problems converting large units of measurement into smaller ones.

For example:

23 m = 2,300 cm = 23,000 mm.

43 kg = 43,000 g.

When it comes to converting smaller units into larger ones, problems usually arise. Let's figure out how best to act in such situations.

Example.

Suppose we need to convert 28 mm to meters. This problem often arises in physics when it is necessary to convert units of measurement to the SI system.

Solution.

We proceed as follows:

1) We build a chain of units of measurement from largest to smallest:

m -> cm -> mm.

2) Remember: 1 m = 100 cm, 1 cm = 10 mm.

3) Now we go in reverse order: 1 mm = 0.1 cm, 1 cm = 0.01 m.

This means 1 mm = 0.1 cm = 0.1 · 0.01 = 0.001 m.

4) 28 mm = 28 0.001 = 0.028 m.

Answer. 28 mm = 0.028 m.

Example.

Suppose we need to convert 25 liters to 3 meters.

Solution.

We use the same scheme.

1) We build a chain of units of measurement from largest to smallest, but for now without cubes.

2) Remember: 1 m = 10 dm.

3) Now we go in reverse order: 1 dm = 0.1 m.

This means 1 liter = 1 dm 3 = 0.001 m 3.

4) 25 liters = 25 dm3 = 25 · 0.001 = 0.025 m3.

Answer. 25 liters = 0.025 m3.

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Pascal (Pa, Pa)

Pascal (Pa, Pa) is a unit of measurement of pressure in the International System of Units (SI system). The unit is named after the French physicist and mathematician Blaise Pascal.

Pascal is equal to the pressure caused by a force equal to one newton (N) uniformly distributed over a surface of one square meter normal to it:

1 pascal (Pa) ≡ 1 N/m²

Multiples are formed using standard SI prefixes:

1 MPa (1 megapascal) = 1000 kPa (1000 kilopascals)

Atmosphere (physical, technical)

The atmosphere is an off-system unit of measurement of pressure, approximately equal to atmospheric pressure on the surface of the Earth at the level of the World Ocean.

There are two approximately equal units with the same name:

1. Physical, normal or standard atmosphere (atm, atm) - exactly equal to 101,325 Pa or 760 millimeters of mercury.

Technical atmosphere (at, at, kgf/cm²)- equal to the pressure produced by a force of 1 kgf, directed perpendicularly and uniformly distributed over a flat surface with an area of ​​1 cm² (98,066.5 Pa).

1 technical atmosphere = 1 kgf/cm² (“kilogram-force per square centimeter”). // 1 kgf = 9.80665 newtons (exact) ≈ 10 N; 1 N ≈ 0.10197162 kgf ≈ 0.1 kgf

On English language kilogram-force is denoted as kgf (kilogram-force) or kp (kilopond) - kilopond, from the Latin pondus, meaning weight.

Notice the difference: not pound (in English “pound”), but pondus.

In practice, they approximately take: 1 MPa = 10 atmospheres, 1 atmosphere = 0.1 MPa.

Bar

A bar (from the Greek βάρος - heaviness) is a non-systemic unit of pressure measurement, approximately equal to one atmosphere. One bar is equal to 105 N/m² (or 0.1 MPa).

Relationships between units of pressure

1 MPa = 10 bar = 10.19716 kgf/cm² = 145.0377 PSI = 9.869233 (physical atm.) = 7500.7 mm Hg.

1 bar = 0.1 MPa = 1.019716 kgf/cm² = 14.50377 PSI = 0.986923 (physical atm.) = 750.07 mm Hg.

1 atm (technical atmosphere) = 1 kgf/cm² (1 kp/cm², 1 kilopond/cm²) = 0.0980665 MPa = 0.98066 bar = 14.223

1 atm (physical atmosphere) = 760 mm Hg = 0.101325 MPa = 1.01325 bar = 1.0333 kgf/cm²

1 mm Hg = 133.32 Pa = 13.5951 mm water column

Volumes of liquids and gases / Volume

1 gl (US) = 3.785 l

1 gl (Imperial) = 4.546 l

1 cu ft = 28.32 l = 0.0283 cubic meters

1 cu in = 16.387 cc

Flow speed

1 l/s = 60 l/min = 3.6 cubic meters/hour = 2.119 cfm

1 l/min = 0.0167 l/s = 0.06 cubic meters/hour = 0.0353 cfm

1 cubic m/hour = 16.667 l/min = 0.2777 l/s = 0.5885 cfm

1 cfm (cubic feet per minute) = 0.47195 l/s = 28.31685 l/min = 1.699011 cubic meters/hour

Throughput / Valve flow characteristics

Flow coefficient (factor) Kv

Flow Factor - Kv

The main parameter of the shut-off and control body is the flow coefficient Kv. The flow coefficient Kv shows the volume of water in cubic meters per hour (cbm/h) at a temperature of 5-30ºC passing through the valve with a pressure loss of 1 bar.

Flow coefficient Cv

Flow Coefficient - Cv

In countries with an inch measurement system, the Cv coefficient is used. It shows how much water in gallons/minute (gpm) at 60ºF flows through a fixture when there is a 1 psi pressure drop across the fixture.

Kinematic viscosity / Viscosity

1 ft = 12 in = 0.3048 m

1 in = 0.0833 ft = 0.0254 m = 25.4 mm

1 m = 3.28083 ft = 39.3699 in

Units of force

1 N = 0.102 kgf = 0.2248 lbf

1 lbf = 0.454 kgf = 4.448 N

1 kgf = 9.80665 N (exactly) ≈ 10 N; 1 N ≈ 0.10197162 kgf ≈ 0.1 kgf

In English, kilogram-force is expressed as kgf (kilogram-force) or kp (kilopond) - kilopond, from the Latin pondus, meaning weight. Please note: not pound (in English “pound”), but pondus.

Units of mass

1 lb = 16 oz = 453.59 g

Moment of force (torque)/Torque

1 kgf. m = 9.81 N. m = 7.233 lbf * ft

Power Units / Power

Some values:

Watt (W, W, 1 W = 1 J/s), horsepower (hp - Russian, hp or HP - English, CV - French, PS - German)

Unit ratio:

In Russia and some other countries 1 hp. (1 PS, 1 CV) = 75 kgf* m/s = 735.4988 W

In the USA, UK and other countries 1 hp = 550 ft*lb/s = 745.6999 W

Temperature

Fahrenheit temperature:

[°F] = [°C] × 9⁄5 + 32

[°F] = [K] × 9⁄5 − 459.67

Temperature in Celsius:

[°C] = [K] − 273.15

[°C] = ([°F] − 32) × 5⁄9

Kelvin temperature:

[K] = [°C] + 273.15

[K] = ([°F] + 459.67) × 5⁄9

Consider the physical record m=4kg. In this formula "m"- designation of a physical quantity (mass), "4" - numerical value or magnitude, "kg"- unit of measurement of a given physical quantity.

There are different types of quantities. Here are two examples:
1) The distance between points, the lengths of segments, broken lines - these are quantities of the same kind. They are expressed in centimeters, meters, kilometers, etc.
2) The durations of time intervals are also quantities of the same kind. They are expressed in seconds, minutes, hours, etc.

Quantities of the same kind can be compared and added:

BUT! It makes no sense to ask what is greater: 1 meter or 1 hour, and you cannot add 1 meter to 30 seconds. The duration of time intervals and distance are quantities of different kinds. They cannot be compared or added together.

Values ​​can be multiplied by positive numbers and zero.

Taking any value e per unit of measurement, you can use it to measure any other quantity A same kind. As a result of the measurement we obtain that A=x e, where x is a number. This number x is called the numerical value of the quantity A with unit of measurement e.

There are dimensionless physical quantities. They do not have units of measurement, that is, they are not measured in anything. For example, friction coefficient.

What is SI?

According to data from Professor Peter Cumpson and Dr Naoko Sano from the University of Newcastle, published in the journal Metrology, the standard kilogram gains on average about 50 micrograms per hundred years, which ultimately can significantly affect many physical quantities.

The kilogram is the only SI unit that is still defined using a standard. All other measures (meter, second, degree, ampere, etc.) can be determined with the necessary accuracy in a physical laboratory. The kilogram is included in the definition of other quantities, for example, the unit of force is the newton, which is defined as a force that changes the speed of a body weighing 1 kg by 1 m/s in 1 second in the direction of the force. Other physical quantities depend on the value of Newton, so in the end the chain can lead to a change in the value of many physical units.

The most important kilogram is a cylinder with a diameter and height of 39 mm, consisting of an alloy of platinum and iridium (90% platinum and 10% iridium). It was cast in 1889 and is kept in a safe at the International Bureau of Weights and Measures in Sèvres near Paris. The kilogram was originally defined as the mass of one cubic decimeter (liter) of pure water at a temperature of 4 °C and standard atmospheric pressure at sea level.

From the standard kilogram, 40 exact copies were initially made, which were distributed throughout the world. Two of them are located in Russia, at the All-Russian Research Institute of Metrology named after. Mendeleev. Later another series of replicas was cast. Platinum was chosen as the base material for the standard because it has high oxidation resistance, high density and low magnetic susceptibility. The standard and its replicas are used to standardize mass in a variety of industries. Including where micrograms are significant.

Physicists believe that the weight fluctuations were the result of atmospheric pollution and changes in the chemical composition of the cylinder surfaces. Despite the fact that the standard and its replicas are stored in special conditions, this does not save the metal from interaction with the environment. The exact weight of the kilogram was determined using X-ray photoelectron spectroscopy. It turned out that the kilogram “gained” by almost 100 micrograms.

At the same time, copies of the standard differed from the original from the very beginning and their weight also changes differently. Thus, the main American kilogram initially weighed 39 micrograms less than the standard, and a check in 1948 showed that it had increased by 20 micrograms. The other American copy, on the contrary, is losing weight. In 1889, kilogram number 4 (K4) weighed 75 mcg less than the standard, and in 1989 it was already 106 mcg.

Since 1963, in the USSR (GOST 9867-61 “International System of Units”), in order to unify units of measurement in all fields of science and technology, the international (international) system of units (SI, SI) has been recommended for practical use - this is a system of units of measurement of physical quantities , adopted by the XI General Conference on Weights and Measures in 1960. It is based on 6 basic units (length, mass, time, force electric current, thermodynamic temperature and luminous intensity), as well as 2 additional units (plane angle, solid angle); all other units given in the table are their derivatives. The adoption of a unified international system of units for all countries is intended to eliminate the difficulties associated with the translation of numerical values ​​of physical quantities, as well as various constants from any one currently operating system (GHS, MKGSS, ISS A, etc.) into another.

Note. Multiple and submultiple units of measurement, with the exception of units of time and angle, are formed by multiplying them by the appropriate power of 10, and their names are added to the names of the units of measurement. It is not allowed to use two prefixes to the name of the unit. For example, you cannot write millimicrowatt (mmkW) or micromicrofarad (mmf), but you must write nanowatt (nw) or picofarad (pf). Prefixes should not be applied to the names of such units that indicate a multiple or submultiple unit of measurement (for example, micron). To express the duration of processes and designate calendar dates of events, the use of multiple units of time is allowed.

The most important units of the International System of Units (SI)

Basic units
(length, mass, temperature, time, electric current, light intensity)

Additional and derived units