International system of units of physical quantities in metrology. Units of measurement of physical quantities. Metrology and technical measurements

General concept.

The branch of science that studies measurements is metrology.

Metrology– the science of measurements, methods and means of ensuring their unity and ways of achieving the required accuracy.

In metrology they decide the following main tasks : development general theory measurement units physical quantities and their systems, development of methods and measuring instruments, methods for determining the accuracy of measurements, the basis for ensuring the unity and uniformity of measuring instruments, standards and exemplary measuring instruments, methods for transferring unit sizes from standards and exemplary measuring instruments to working measuring instruments.

Physical quantities. International system units of physical quantities Si.

Physical quantity is a characteristic of one of the properties of a physical object (phenomenon or process), common in qualitative terms to many physical objects, but quantitatively individual for each object.

Physical quantity value is an assessment of its value in the form of a certain number of units accepted for it or a number on a scale accepted for it. For example, 120 mm is a linear value; 75 kg is the body weight value, HB190 is the Brinell hardness number.

Measuring a physical quantity called a set of operations performed using technical means storing a unit, or reproducing the scale of a physical quantity, which consists of comparing (explicitly or implicitly) the measured quantity with its unit or scale in order to obtain the value of this quantity in the form most convenient for use.

In measurement theory it is generally accepted five types of scales : names, order, intervals, relations and absolute.

You can select three types of physical quantities , the measurement of which is carried out according to various rules.

The first type of physical quantities includes quantities on the set of sizes of which only relations of order and equivalence are defined. These are relations such as “softer”, “harder”, “warmer”, “colder”, etc. Values ​​of this kind include, for example, hardness, defined as the ability of a body to resist the penetration of another body into it; temperature as the degree of heating of a body, etc. The existence of such relationships is established theoretically or experimentally using special means of comparison, as well as on the basis of observations of the results of the influence of a physical quantity on any objects.

For the second type of physical quantities, the relation of order and equivalence takes place both between sizes and between dimensions in pairs of their sizes. Hook. Differences in time intervals are considered equal if the distances between the corresponding marks are equal.

The third type consists of additive physical quantities. Additive physical quantities are quantities on the set of sizes of which not only the relations of order and equivalence, but also the operations of addition and subtraction are defined. Such quantities include length, mass, current, etc. They can be measured in parts, and also reproduced using a multi-valued measure based on the summation of individual measures. For example, the sum of the masses of two bodies is the mass of the body that balances the first two on equal-armed scales.

System of physical quantities is a set of interrelated physical quantities, formed in accordance with accepted principles, when some quantities are taken as independent, while others are functions of independent quantities. A system of physical quantities contains basic physical quantities, conventionally accepted as independent of other quantities of this system, and derived physical quantities, determined through the basic quantities of this system.

Additive physical quantities are quantities on the set of sizes of which not only the relations of order and equivalence, but also the operations of addition and subtraction are defined. Such quantities include length, mass, current, etc. They can be measured in parts, and also reproduced using a multi-valued measure based on the summation of individual measures. For example, the sum of the masses of two bodies is the mass of the body that balances the first two on equal-armed scales.

Basic physical quantity is a physical quantity included in the system of units and conventionally accepted as independent of other quantities of this system.

Derived unit of the system of units – a unit of a derivative of a physical quantity of a system of units, formed in accordance with an equation relating it to the base units.

The derived unit is called coherent, if in this equation the numerical coefficient is taken equal to one. Accordingly, a system of units consisting of basic units and coherent derivatives is called a coherent system of units of physical quantities.

Absolute scales have all the features of ratio scales, but in addition they have a natural, unambiguous definition of the unit of measurement. Such scales correspond to relative quantities (ratios of the same physical quantities described by ratio scales). Among the absolute scales, absolute scales are distinguished, the values ​​of which are in the range from 0 to 1. Such a value is, for example, the efficiency factor.

Name scales characterized only by an equivalence relation. At its core, it is qualitative and does not contain zeros or units of measurement. An example of such a scale is the assessment of color by name (color atlases). Since each color has many variations, such a comparison can only be made by an experienced expert with appropriate visual capabilities.

Order scales characterized by the relation of equivalence and order. For practical use For such a scale it is necessary to establish a number of standards. Classification of objects is carried out by comparing the intensity of the assessed property with its reference value. Order scales include, for example, the earthquake scale, the wind force scale, the hardness scale, etc.

Difference scale differs from the order scale in that in addition to the relations of equivalence and order, the equivalence of intervals (differences) between various quantitative manifestations of the property is added. It has conditional zero values, and the size of the intervals is established by agreement. A typical example of such a scale is the time interval scale. Time intervals can be summed (subtracted).

Attitude scales describe properties to which the relations of equivalence, order and summation, and, consequently, subtraction and multiplication, apply. These scales have a natural zero value, and the units of measurement are established by agreement. For a ratio scale, one standard is sufficient to distribute all objects under study according to the intensity of the property being measured. An example of a ratio scale is the mass scale. The mass of two objects is equal to the sum of the masses of each of them.

Unit of physical quantity– a physical quantity of a fixed size, which is conventionally assigned a value equal to one, and is used for the quantitative expression of homogeneous physical quantities. The number of independently established quantities is equal to the difference between the number of quantities included in the system and the number of independent equations for the connection between quantities. For example, if the speed of a body is determined by the formula υ =L/t then only two quantities can be established independently, and the third can be expressed through them.

Dimension of a physical quantity– an expression in the form of a power monomial, composed of products of symbols of basic physical quantities in various powers and reflecting the relationship of a given quantity with physical quantities accepted in a given system of quantities as basic, and with a proportionality coefficient equal to unity.

The powers of the symbols of the basic quantities included in the monomial can be integer, fractional, positive and negative.

The dimension of quantities is denoted by the sign dim. In system LMT dimension of quantities X will:

Where L, M, T - symbols of quantities taken as basic (length, mass, time, respectively); l, m, t– integer or fractional, positive or negative real numbers, which are indicators of dimension.

The dimension of a physical quantity is more general characteristic than the equation that determines the quantity, since the same dimension can be inherent in quantities that have different qualitative aspects.

For example, the work of force A is determined by the equation A = FL; kinetic energy of a moving body - by the equation E k = mυ 2 /2, and the dimensions of the first and second are the same.

Various operations can be performed on dimensions: multiplication, division, exponentiation and root extraction.

Basic SI units

Indicator of the dimension of a physical quantity – exponent to which the dimension of a basic physical quantity included in the dimension of a derivative physical quantity is raised. Dimensions are widely used in forming derived units and checking the homogeneity of equations. If the weight of the exponents of a dimension is equal to zero, then such a physical quantity is called dimensionless. All relative quantities (the ratio of quantities of the same name) are dimensionless. Taking into account the need for the International System of Units to cover all areas of science and technology, it has selected units as the main ones. In mechanics these are the units of length, mass and time; in electricity a unit of force is added electric current, in heat - a unit of thermodynamic temperature, in optics - a unit of luminous intensity, in molecular physics, thermodynamics and chemistry – a unit of quantity of a substance. These seven units are respectively: meter, kilogram, second, ampere. Kelvin, candela and mole are chosen as the SI base units.

An important principle, which is observed in the International System of Units, is its coherence(consistency). Thus, the choice of the main units of the system ensured complete consistency of mechanical and electrical units. For example, watt– a unit of mechanical power (equal to the joule per second) is equal to the power generated by an electric current of 1 ampere at a voltage of 1 volt. For example, the unit of speed is formed using an equation that determines the speed of a rectilinearly and uniformly moving point

υ =L/t, Where

υ - speed, L– length of the traveled path, t – time. Substitution instead υ , L And t and their SI units will give ( υ }={L)/{t) = 1 m/s. Therefore, the SI unit of speed is meter per second. He equal to speed rectilinearly and uniformly moving point, at which this point in time t = 1s moves a distance L= 1m. For example, to form a unit of energy it is used

the equation T = tυ e,Where T- kinetic energy; T- body mass; t is the speed of motion of a point, then the coherent SI unit of energy is formed as follows:

Derived SI units


Related information.


To eliminate the arbitrary choice of units of physical quantities, to ensure a uniform expression and adequate understanding of the quality of parameters, characteristics and properties of various objects, processes, states, i.e. in order to ensure the conditions for uniformity of measurements, units of physical quantities must be generally accepted and generally accepted. These requirements are fully met by the International System of Units of Physical Quantities (SI), which is modern form presentation and development of the metric system of measures.

The advantages of the SI system are:

  • ? universality, which implies its coverage of all areas of science, technology, and production; all derived units are formed according to a single rule. This makes it possible to create new derivative units as science and technology develop;
  • ? coherence, which allows you to simplify calculation formulas to a minimum by eliminating conversion factors (when the numerical factor is equal to 1). For example, the speed of movement of bodies can be expressed by the relation V = = L/t, Where L- path length in meters; t- movement time in seconds. Substituting the dimensions of the indicated quantities into the formula gives V== 1m/s;
  • ? unification of units of all areas of measurement, which is understood as bringing units to uniformity on the basis of a rational reduction in the number of their varieties.

Based on their conditional dependence on other quantities, units are divided into basic (independent physical quantities located in the basic system of units) and derivatives (conditionally dependent on the basic quantities).

There are seven primary and two supplementary units in the SI system. Additional units are used to form derived units depending on certain conditions, associated with plane and solid angles.

The main and additional units of the International System are given in Table. 1.1.

Table 1.1

International System (SI) units

Name

physical

quantities

Designation

physical

quantities

Unit name

Designation

international

Basic units

kilogram

Electric current strength

Thermodynamic temperature

Ending

The decisions of the General Conference on Weights and Measures established the following definitions basic units:

U meter - the length of the path traveled by light in a vacuum in 1/299792458 of a second;

  • ? kilogram - a unit of mass equal to the mass of the international prototype of the kilogram;
  • ? a second is equal to 9,192,631,770 periods of radiation corresponding to the transition between two hyperfine levels of the ground state of the cesium-133 atom;
  • ? ampere equal to force unchanging current, which, passing through two normal parallel conductors of infinite length and negligibly small circular cross-sectional area, located in a vacuum at a distance of 1 m from each other, causes an interaction force between the conductors equal to 2 10 7 N for each meter of length;
  • ? kelvin - a unit of thermodynamic temperature equal to 1/273.16 of the thermodynamic temperature of the triple point of water;
  • ? candela is equal to the luminous intensity in a given direction of a source emitting monochromatic radiation with a frequency of 540 10 12 Hz, the luminous energy intensity of which in this direction is 1/683 W/sr;
  • ? mole - amount of substance in a system containing the same amount structural elements, how many atoms are contained in carbon-12 weighing 0.012 kg.

Additional units- These are units of plane and solid angles (radians and steradians). They are not included in the main ones due to difficulties in interpreting the dimensions of quantities associated with rotation.

They cannot be classified as derivatives, since they do not depend on the basic quantities. These units are independent of the size of the unit of length.

Radian- unit of plane angle, equal to angle between two radii of a circle, the length of the arc between which is equal to the radius. In degrees, 1 rad = 57° 17"45".

Steradian - a unit equal to the solid angle with the vertex at the center of the sphere, cutting out the area on the surface of the sphere, equal to the area square with a side equal to the radius of the sphere.

Derived units SI units are formed from basic and additional units based on equations between physical quantities. Derived SI units with special names are given in table. 1.2.

Table 1.2

Derived SI units with special names

Name of quantity

Name

Designation

international

Strength, weight

Mechanical stress pressure, elastic modulus

Energy, work, amount of heat

Power, energy flow

W

Electrical voltage, electrical potential, electromotive force, electrical potential difference

Electrical capacity

Electrical resistance

Electrical conductivity

Magnetic induction flux, magnetic flux

Magnetic flux density, magnetic induction

Inductance, mutual inductance

Light flow

Ending

In order to avoid obtaining too large or small values ​​of physical quantities, the SI establishes the use of decimal multiples and submultiples of SI units, which are formed using multipliers and contain prefixes corresponding to the multipliers (Table 1.3).

Table 1.3

Unit multipliers and prefixes

Factor

Console

Prefix designation

international

The names of multiple and submultiple units of physical quantities formed in this way are written together with the name of the main or derived SI unit, for example, kilometer - km, megawatt - MW, micrometer - micrometer, millivolt - mV, etc. Two or more prefixes cannot be used.

Kolchkov V.I. METROLOGY, STANDARDIZATION AND CERTIFICATION. M.: Textbook

3. Metrology and technical measurements

3.3. International system of units of physical quantities

The Harmonized International System of Units of Physical Quantities was adopted in 1960 by the XI General Conference on Weights and Measures. International system - SI (SI), SI - initial letters French name Systeme International. The system provides a list of seven basic units: meter, kilogram, second, ampere, kelvin, candela, mole and two additional ones: radian, steradian, as well as prefixes for the formation of multiples and submultiples.

3.3.1 SI base units

  • Meter equal to the length of the path traveled by light in a vacuum in 1/299.792.458 of a second.
  • Kilogram equal to mass international prototype of the kilogram.
  • Second equal to 9.192.631.770 periods of radiation corresponding to the transition between two hyperfine levels of the ground state of the cesium-133 atom.
  • Ampere is equal to the force of an electric current that does not change in time, which, when passing through two parallel straight conductors of infinite length and a negligibly small circular cross-sectional area, located at a distance of 1 m from each other in a vacuum, causes an interaction force equal to 2 on each section of the conductor 1 m long 10 to the minus 7th power N.
  • Kelvin equal to 1/273.16 of the thermodynamic temperature of the triple point of water.
  • Mole equal to the amount of substance in a system containing the same number of structural elements as there are atoms in carbon-12 weighing 0.012 kg.
  • Candela equal to the luminous intensity in a given direction of a source emitting monochromatic radiation with a frequency of 540 10 to the 12th power of Hz, the energetic luminous intensity of which in this direction is 1/683 W/sr.

Table 3.1. SI Major and Supplementary Units

Basic SI units

Magnitude

Designation

Name

Name

international

kilogram

Electric current strength I

Thermodynamic
temperature

The power of light

Quantity of substance

Derived SI units

Magnitude

Designation

Name

Name

international

Flat angle

Solid angle

steradian

3.3.2. Derived SI units

Derived units of the International System of Units are formed using the simplest equations between physical quantities in which the numerical coefficients are equal to unity. For example, to determine the dimension linear speed Let's use the expression for the speed of a uniform rectilinear movement. If the length of the distance traveled is v = l/t(m), and the time during which this path is covered is t(s), then the speed is obtained in meters per second (m/s). Consequently, the SI unit of speed - meter per second - is the speed of a rectilinearly and uniformly moving point, at which it moves a distance of 1 m in 1 s. Other units are formed in a similar way, incl. with a coefficient not equal to one.

Table 3.2. Derived SI units (see also Table 3.1)


Derived SI units with their own names

Name

Expressing a derived unit in terms of SI units

Magnitude

Name

Designation

other units

basic and additional units

s–1

m kg s–2

Pressure

N/m2

m–1 kg s–2

Energy, work,

m2 kg s–2

Power

m2 kg s–3

Electr. charge

Electric potential

m2 kg s–3 A–1

Electr. capacity

m–2 kg–1 s4 A2

El..resistance

m2 kg s–3 A–2

Electrical conductivity

m–2 kg–1 s3 A2

Magnetic induction flux

m2 kg s–2 A–1

Units of physical quantities- specific physical quantities, conventionally accepted as units of physical quantities.

A physical quantity is understood as a characteristic physical object, common for many objects in a qualitative sense (for example, length, mass, power) and individual for each object in quantitatively(for example length nerve fiber, human body weight, absorbed dose rate of ionizing radiation). There is a natural connection between the physical quantities that characterize any object. The establishment of this connection through the measurement of physical quantities was of great scientific and practical importance. The measurement of a physical quantity means a set of experimental (using measures and standards) and, in some cases, computational operations to determine the quantity of a given quantity. In this case, a justified rational choice of its unit is important.

The history of the development of metrology indicates that most of the old units of length, area, volume, mass, time and other quantities were chosen arbitrarily, without taking into account any internal connection between them. This led to the emergence of different countries a world of many different units for measuring the same physical quantities. Thus, length was measured in arshins, elbows, feet, inches, mass - in ounces, pounds, spools, etc. In a number of cases, units were chosen based on the convenience of measurement technology or practical application. This is how, for example, a millimeter of mercury and horsepower appeared. The intensive and initially independent development of individual fields of science and technology in various countries at the beginning of the 19th century, the formation of new branches of knowledge contributed to the emergence of new physical quantities and, accordingly, many new units. The multiplicity of units of measurement was a serious obstacle to the further development of science and the growth of material production; The lack of unity in the understanding, definition and designation of physical quantities complicated international trade relations and hampered scientific and technological progress in general. All this caused the need for strict unification of units and the development of systems of units of physical quantities convenient for widespread use. The construction of such a system was based on the principle of selecting a small number of basic units, independent of each other, on the basis of which, with the help of mathematical relationships expressing natural connections between physical quantities, the remaining units of the system were established.

Attempts to create a unified system of units have been made repeatedly. Were created Metric system measures, systems ISS, ISS, MKGSS, GHS, etc. However, each of these systems individually did not provide the possibility of using it in all areas of scientific and practical human activity, and parallel use various systems created, among other inconveniences, certain difficulties in mutual recalculations. Various international scientific and technical organizations working in the field of metrology during the second half of the 19th century. and in the first half of the 20th century. prepared the way for the creation of a unified international system of units, and on October 7, 1958, the International Committee of Legal Metrology announced the establishment of this system.

By decision of the General Conference on Weights and Measures in 1960, a universal system of units of physical quantities was adopted. called "Systeme internationale d"unites" (International System of Units) or abbreviated SI (in Russian transcription SI). The CMEA Standing Commission on Standardization approved the fundamental standard "Metrology. Units of physical quantities. ST CMEA 1052-78", the author and developer of which is the USSR. The standard was established by the Resolution of the CMEA member countries since 1979-1980. State Committee USSR according to the standards of March 19, 1981, the CMEA standard was replaced State standard GOST 8.417-81 (ST SEV 1052-78) “Units of physical quantities”, put into effect on January 1, 1982. GOST established a list of E. f. V. for use in the USSR, their name and designation, as well as the procedure for using non-system units and excluding a number of non-system units subject to withdrawal. The use of SI has become mandatory in all areas of science and technology, as well as in the national economy.

Structure of the International System of Units (SI). The International System of Units is a set of basic and derived units covering all areas of measurement of mechanical, thermal, electrical, magnetic and other quantities. An important advantage of this system is also that its constituent basic and derived units are convenient for practical purposes. The main advantage of SI is its coherence (consistency), i.e. all derived units in it are obtained using defining formulas (the so-called dimension formulas) by multiplying or dividing the basic units without introducing numerical coefficients showing how many times the value of the derived unit increases or decreases when the values ​​of the basic units change. for example, for a unit of speed it has the following form: v = kL×T-1~; Where k- proportionality coefficient equal to 1 , L- path length, T- time. If instead L And T Substitute the names of the units of measurement of length and time in the SI system, and we obtain the formula for the dimension of the unit of speed in this system: V = m/s, or v = m×s-1 . If a physical quantity is a ratio of two dimensional quantities of the same nature, then it has no dimension. Such dimensionless quantities are, for example, the refractive index, mass or volume fraction of a substance.

Units of physical quantities that are established independently of others and on which the system of units is based are called the basic units of the system. Units defined using formulas and equations that relate physical quantities to each other are called derived units of the system. Basic or derived units included in a system of units are called system units.

The International System of Units includes 7 main ones ( table 1 ), 2 additional ( table 2 ), as well as derived units formed from basic and additional units ( table 3 and 4 ). Additional units (radians and steradians) are independent of the basic units and have zero dimension. They are not used for direct measurements due to the lack measuring instruments, graduated in radians and steradians. These units are used for theoretical research and calculations.

Table 1.

Basic SI units and the quantities they measure

Unit name

Designation

Measured quantity

international

Kilogram

Electric current strength

Thermodynamic temperature*

mole

Quantity of substance

The power of light

* The name “Kelvin temperature” is also acceptable. In addition to the Kelvin temperature ( T) you can use Celsius temperature ( t), determined from the expression: t = T – T 0 Where T- thermodynamic temperature, T 0= 273.15 K. For a temperature difference of 1°C = 1 K.

Table 2.

Additional SI units and quantities they measure

Unit name

Designation

Measured quantity

international