Key Words

1 Constants and Conversion Factors

Table 1

2 Basic and Supplementary Units

  • A meter (m) is 1,650,763.73 wavelengths in vacuo of the radiation corresponding to the transition between the energy levels 2p10 and 5d5 of the krypton 86 atom.

  • A kilogram (kg) is the mass of the international prototype in the custody of the Bureau International des Poids et Mesures at Sevres in France.

  • A second (sec) is the interval occupied by 9,192,631,770 cycles of the radiation corresponding to the transition of the cesium-133 atom when unperturbed by exterior fields.

  • An ampere is the constant current that if maintained in two parallel rectilinear conductors of infinite length of negligible circular cross section and placed at a distance of one meter apart in vacuo would produce between these conductors a force equal to 2 × 10−7 newton per meter length.

  • A kelvin (°K) is the degree interval of the thermodynamic scale on which the temperature of the triple point of water is 273.16 degrees.

  • A candle is such that the luminance of a full radiator at the temperature of solidification of platinum is 60 units of luminous intensity per square centimeter.

  • A mole (mol) is the amount of substance which contains as many elementary units as there are atoms in 0.012 kg of carbon-12. The elementary unit must be specified and may be an atom, an ion, an electron, a photon, etc., or a given group of such entities.

  • A radian is the angle subtended at the center of a circle by an arc of the circle equal in length to the radius of the circle.

  • A steradian is the solid angle that, having its vertex at the center of a sphere, cuts off an area of the surface of the sphere equal to that of a square with sides of length equal to the radius of the sphere.

3 Derived Units and Quantities

  • The liter was defined in 1901 as the volume of 1 kilogram of pure water at normal atmospheric pressure and maximum density equal therefore to 1.000028 dm3. This 1901 definition applied for the purpose of the 1963 Weights and Measures Acts.

  • By a resolution of the 12th Conference General des Poids et Mesures (CGPM) in 1964 the word liter is now recognized as a special name for the dm3, but is not used to express high precision measurements. It is used widely in engineering and the retail business, where the discrepancy of 28 parts in 1 million is of negligible significance.

  • A newton (N) is the force that, when applied to a body of mass of one kilogram, gives it an acceleration of one meter per second per second.

    Stress is defined as the resultant internal force per unit area resisting change in the shape or size of a body acted on by external forces, and is therefore measured in newtons per square meter (N/m2).

  • A bar is a pressure equivalent to 100,000 newtons acting on an area of one square metor.

  • A joule (J) is the work done when the point of application of a force of one newton is displaced through a distance of one meter in the direction of the force.

  • A watt is equal to one joule per second.

  • Dynamic viscosity is the property of a fluid whereby it tends to resist relative motion within itself. It is the shear stress, i.e., the tangential force on unit area, between two infinite horizontal planes at unit distance apart, one of which is fixed while the other moves with unit velocity. In other words, it is the shear stress divided by the velocity gradient, i.e., (N/m2) ÷ (m/sec/m) = N sec/m2.

  • Kinematic viscosity is the dynamic viscosity of a fluid divided by its density, i.e., (N sec/m2)/(kg/m3) = m2/sec.

  • Density of heat flow rate (or heat flux) is the heat flow rate (W) per unit area, i.e., W/m2.

  • Coefficient of heat transfer is the heat flow rate (W) per unit area per unit temperature difference, i.e., W/m2° C.

  • Thermal conductivity is the quantity of heat that will be conducted in unit time through unit area of a slab of material of unit thickness with a unit difference of temperature between the faces; in other words, the heat flow rate (W) per unit area per unit temperature gradient, i.e., W/[m2(° C/m)] = W/m° C.

  • The heat capacity of a substance is the quantity of heat gained or lost by the substance per unit temperature change, i.e., J/° C.

  • Specific heat capacity is the heat capacity per unit mass of the substance, i.e., J/kg° C.

  • Internal energy is the kinetic energy possessed by the molecules of a substance due to temperature and is measured in joules (J).

  • Specific internal energy (u) is the internal energy per unit mass of the substance, i.e., J/kg. When a small amount of heat is added at constant volume the increase in specific internal energy is given by: du = c v dT, where c v is the specific heat capacity at constant volume, and dT is the increase in absolute temperature.

  • Specific enthalpy (h) is defined by the equation: h = u + pv, where p is the pressure and v is the specific volume. Specific enthalpy is measured in J/kg. When a small amount of heat is added to a substance at constant pressure, the increase in specific enthalpy is given by: −dh = cp dT, where cp is the specific heat capacity at constant pressure.

  • The specific latent heat of a substance is the heat gained per unit mass without an accompanying rise in temperature during a change of state at constant pressure. It is measured in J/kg.

  • The entropy (S) of a substance is such that when a small amount of heat is added, the increase in entropy is equal to the quantity of heat added (dQ) divided by the absolute temperature (T) at which the heat is absorbed; i.e., dS = dQ/T, measured in J/°K.

  • The specific entropy (s) of a substance is the entropy per unit mass, i.e., J/kg°K.

  • A volt is the difference of electric potential between two points of a conductor carrying a constant current of one ampere when the power dissipated is one watt.

  • A weber (Wb) is the magnetic flux through a conductor with a resistance of one ohm when reversal of the direction of the magnetic flux causes the transfer of one coulomb in the conductor loop.

  • Tesla: The magnetic flux density is the normal magnetic flux per unit area and is measured in teslas.

  • A lumen, the unit of luminous flux, is the flux emitted within unit solid angle of one steradian by a point source having a uniform intensity of one candle.

  • A lux is an illumination of one lumen per square meter.

  • Luminance is the luminous intensity per unit area of a source of light or of an illumination. It is measured in candles per square meter.

4 Physical Constants

Standard temperature and pressure (S.T.P.)

\(\left\{\begin{array}{ll}= {273.15^{\circ} {\rm K} \ {\rm and\ 1}.013 \times 10^5 {\rm N/m^2}}\\= 0^\circ \text{C and 1}\text{.013 bar}\\= 0^\circ\text{C and 760 mmHg}\end{array}\right.\)

Molecular volume of ideal gas at S.T.P.

= 22.4 litres/mol

Gas constant (R)

= 8.314 J/mol° K

RT(273.15°K)

= 2.271 × 103 J/mol

Avogadro constant

= 6.023 × 1023/mol

Boltzmann constant

= 1.3805 × 10−23 J/K

Faraday constant

= 9.6487 × 104°C/mol (= A s/mol)

Planck constant

= 6.626 × 10−34 J sec

Stefan-Boltzman constant

= 5.6697 × 10−8 W/m2 K4

Ice point of water

= 273.15°K (0°C)

Triple point of water

= 273.16°K (0.01°C)

Speed of light

= 2.998 × 108 m/sec

Acceleration of gravity (Standard) (Greenwich)

\(\begin{array}{lll}\left\{\begin{array}{ll}=9.80665\kern0.5em \mathrm{m}/\mathrm{{s}}^2\hfill \\=9.81188\kern0.5em \mathrm{m}/\mathrm{{s}}^2\end{array}\right. \left[\begin{array}{ll} \mathrm{take}\ \mathrm{g}\ \mathrm{as} \\ {}\hfill 9.81\ \mathrm{m}/\mathrm{{s}}^2\end{array}\right]\end{array}\)

Universal constant of gravitation

= 6.670 × 10−11 Newton m2/kg2

Mass of hydrogen atom

= 1.6734 × 10−27 kg

5 Properties of Water

Table 3 U.S. Customary Units

SI Units

Temperatue, (°C)

Specific weight, γ (kN/m3)

Mass density, ρ (kg/m3)

Dynamic viscosity, μ × 103 (N · s/m2)

Kinematic viscosity, ν × 106 (m2/s)

Surface tensiona, σ (N/m)

Vapor pressure,p ν (kN/m2)

Bulk modulusb, E × 10−6 (kN/m2)

0

9.805

999.8

1.781

1.785

0.0765

0.61

1.98

5

9.807

1000.0

1.518

1.519

0.0749

0.87

2.05

10

9.804

999.7

1.307

1.306

0.0742

1.23

2.10

15

9.798

999.1

1.139

1.139

0.0735

1.70

2.15

20

9.789

998.2

1.002

1.003

0.0728

2.34

2.17

25

9.777

997.0

0.890

0.893

0.0720

3.17

2.22

30

9.764

995.7

0.798

0.800

0.0712

4.24

2.25

40

9.730

992.2

0.653

0.658

0.0696

7.38

2.28

50

9.689

988.0

0.547

0.553

0.0679

12.33

2.29

60

9.642

983.2

0.466

0.474

0.0662

19.92

2.28

70

9.589

977.8

0.404

0.413

0.0644

31.16

2.25

80

9.530

971.8

0.354

0.364

0.0626

47.34

2.20

90

9.466

965.3

0.315

0.326

0.0608

70.10

2.14

100

9.399

958.4

0.282

0.294

0.0589

101.33

2.07

  1. aIn contact with air; b At atmospheric pressure.

6 Periodic Table of the Elements (Compliments of the Lenox Institute of Water Technology)