1
Homogeneity of Relationships and Conversion of Units

1.1 Introduction

The creation of a system of units requires the definition of basic units, their values, and the units derived from them. In mechanics, the units used are length, mass and time, but other options are possible as well, such as length and time, force and time, or mass, speed and time.

The first general conference on weights and measures was held in 1889 at the headquarters of the BPIM (Bureau international des poids et mesures or International Office of Weights and Measures), at the Breteuil pavilion in Sevres (in the suburbs of Paris). In this conference, new international prototypes of the meter and kilogram were officially adopted and filed with the Office.

In 1960, the 11th General Conference of Weights and Measures established the International System (SI), in which the rules for prefixes, derived units and other indications were established. The SI is based on a choice of seven well-defined base units that the convention considered dimensionally independent: the meter, the kilogram, the second, the ampere, the kelvin, the mole and the candela. Derived units are formed by combining the base units according to the algebraic relationships connecting the corresponding quantities. The names and symbols of some of these units may be replaced by special names and symbols, which may be used to express the names and symbols of other derived units.

In November 2018, the International System of units later underwent a significant revision at the 26th General Conference of weights and measures, the culmination of nearly 250 years of consideration given to finding the best way to define a system of units of measurement that would best reflect the natural world.

The General Conference of weights and measures, established at the end of the 19th Century, meets every four to six years to discuss, and possibly modify, the SI, standardizing the units on a global scale. The new changes were applied as of May 20, 2019.

Table 1.1. Basic SI units

1.2 Definitions of the basic SI units

1.2.1 Definition of the meter as adopted in 1983

The "meter" is the "length" of the distance light travels in a vacuum for a period of 1/299792458ths of a second. From this, it can be determined that the speed of light in a vacuum is exactly: c0 = 299,792,458 m/s.

1.2.2 Definition of the kilogram

The "kilogram" is the unit of mass. It is equal to the mass of the international prototype of the kilogram. The term "weight" refers to a quantity that is of the same nature as a force; the weight of a body is the product of the mass of that body multiplied by the acceleration due to gravity. Specifically, the normal weight of a body is the product of the mass of this body multiplied by the normal acceleration from gravity. The number adopted by the International Service of Weights and Measures for the value of normal acceleration from gravity is 980.665 m/s2.

The kilogram is currently defined as the mass of an Iridium platinum cylinder (90% platinum and 10% iridium) 39 mm in diameter and 39 mm high declared the SI unit of mass in 1889 by the BIPM. This unit of measurement is the last SI unit to be defined using a man-made physical standard. It is stored under three sealed glass bells, and it is only removed from this covering for calibrations (an operation that has taken place only three times since its creation). As of May 20, 2019, the kilogram has been defined on the basis of Planck's constant (h)1 from quantum physics, measured on the Kibble2,3 scale at 6.626069934 × 10-34 kg.m2.s-1.

1.2.3 Definition of the second adopted in 1967

The "second" has the duration of 9,192,631,770 periods of radiation from the transition between the two hyperfine levels of the base state of a cesium 133 atom. As a result, the frequency of the hyperfine transition of the base state of the cesium atom is equal to 9,192,631,770 hertz (Hz). Thus, we obtain exactly V (hfs4 Cs) = 9,192,631,770 Hz. At its 1997 session, the International Committee on Weights and Measures confirmed that this definition refers to a cesium atom at rest, at a temperature of 0 K (Kelvin4).

1.2.4 Definition of the ampere adopted in 1948

The "ampere"5 is the intensity of a constant current that is produced between two parallel conductors following straight lines of infinite length and of a negligible circular cross-section placed at a distance of 1 meter from each other in a vacuum between these conductors, a force equal to 2.10-7 newtons6 per meter of length. As a result, the magnetic constant, also known as vacuum permeability, is equal to exactly 4n.10-7 Henrys7 per meter (4n.10-7 H/m). The Ampere is linked to the elementary charge (e), the electric charge of a proton. The mole, the unit for quantities of matter, used mainly in chemistry, is defined directly through the determining of Avogadro's number (AN)8.

1.2.5 Definition of Kelvin adopted in 1967

The Kelvin, a unit of thermodynamic temperature, is the fraction (1/273.16) of the thermodynamic temperature of the triple point of water. As a result, the thermodynamic temperature of the triple point of water is exactly 273.16 Kelvin (273.16 K). Other changes that were made: the Kelvin scale, measured based on water, was redefined based on the Boltzmann9 constant (k), related to the measurement of the thermal agitation of the fundamental constituents of a body.

1.2.6 Definition of a mole

The mole10 is the amount of matter in a system containing as many indivisible entities as there are atoms in 0.012 kilograms of carbon 12; the symbol for this unit is "mol". When using the mole, the individual entities must be specified, and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles. In this definition, it is understood that this refers to unlinked carbon 12 atoms, at rest, and in their base state. As a result, the molar mass of carbon 12 is equal to 0.012 kilograms per mole (0.012 g/mol).

1.2.7 Definition of the candela adopted in 1979

The Candela11 measures the luminous intensity in a given direction of a source that emits energy in monochromatic rays in that direction; it is 1/6, 831ths of a watt12 per steradian13. From this, it can be determined that the spectral luminous efficiency of monochromatic rays of a frequency of 540×1012 hertz is equal to 683 lumens14 per watt (683 lm/W = 683 Sr/W).

1.3 Additional quantities and SI derived quantities

Table 1.2 gives the two additional quantities that have been introduced to ensure the coherence of the system.

Table 1.3 shows the derived quantities in the International System generally used in fluid mechanics and heat transfer.

Table 1.2. SI derived quantities

Table 1.3. Some of the SI derived quantities used in fluid mechanics and heat transfer