BS-5775-2-1993 ISO-31-2-1992.pdf

BRITISH STANDARD BS 5775-2: 1993 ISO 31-2:1992 Specification for Quantities, units and symbols Part 2: Periodic and related phenomena UDC 389.15/.16:534 + 535 + 537.081:006.72 Licensed Copy: sheffieldun sheffieldun, na, Fri Dec 01 10:01:13 GMT+00:00 2006, Uncontrolled Copy, (c) BSI BS 5775-2:1993 This British Standard, having been prepared under the direction of the Systems Department Steering Committee, was published under the authority of the Standards Board and comes into effect on 15 March 1993 © BSI 02-1999 First published September 1979 Second edition March 1993 The following BSI references relate to the work on this standard: Committee reference S/1 Draft for comment 90/51780 DC ISBN 0 580 21996 8 Committees responsible for this British Standard The preparation of this British Standard was entrusted by the Systems Department Steering Committee (S/-) to Technical Committee S/1, upon which the following bodies were represented: Chartered Institution of Building Services Engineers Department of Trade and Industry (National Physical Laboratory) Department of Trade and Industry (National Weights and Measures Laboratory) EEA (the Association of Electronics, Telecommunications and Business Equipment Industries) Institute of Physics Institute of Trading Standards Administration Institution of Chemical Engineers Institution of Electrical Engineers Institution of Mechanical Engineers Institution of Structural Engineers Royal Society Royal Society of Chemistry Schools Mathematics Project Society of Chemical Industry Amendment issued since publication Amd. No.DateComments Licensed Copy: sheffieldun sheffieldun, na, Fri Dec 01 10:01:13 GMT+00:00 2006, Uncontrolled Copy, (c) BSI BS 5755-2:1993 © BSI 02-1999i Contents Page Committees responsibleInside front cover National forewordii 0Introduction1 1Scope2 2Normative reference2 3Names and symbols2 List of referencesInside back cover Licensed Copy: sheffieldun sheffieldun, na, Fri Dec 01 10:01:13 GMT+00:00 2006, Uncontrolled Copy, (c) BSI BS 5775-2:1993 ii © BSI 02-1999 National foreword This Part of BS 5775 has been prepared under the direction of the Systems Department Steering Committee. It is identical with ISO 31-2:1992 Quantities and units Part 2: Periodic and related phenomena, published by the International Organization for Standardization (ISO). ISO 31-2 was prepared by Technical Committee ISO/TC 12 “Quantities, units, symbols, conversion factors” with the active participation and approval of the UK. This Part of BS 5775 supersedes BS 5775-2:1979, which is withdrawn. The principal changes made in this revised version are as follows: a) the decision by the International Committee for Weights and Measures (Comité International des Poids et Mesures, CIPM) in 1980 concerning the status of supplementary units has been incorporated; b) the unit ångström, Å, in use temporarily, has been transferred to the “Conversion factors and remarks” column; c) the special remark on logarithmic quantities and units has been elaborated. BS 5775 comprises the following Parts, each of which is identical with the corresponding Part of ISO 31. Part 0: General principles; Part 1: Space and time; Part 2: Periodic and related phenomena; Part 3: Mechanics; Part 4: Heat; Part 5: Electricity and magnetism; Part 6: Light and related electromagnetic radiations; Part 7: Acoustics; Part 8: Physical chemistry and molecular physics; Part 9: Atomic and nuclear physics; Part 10: Nuclear reactions and ionizing radiations; Part 11: Mathematical signs and symbols for use in the physical sciences and technology; Part 12: Characteristic numbers; Part 13: Solid state physics. Cross-reference The Technical Committee has reviewed the provisions of IEC 27-1:1971, to which normative reference is made in the text and has decided that they are acceptable for use in conjunction with this standard. A British Standard does not purport to include all the necessary provisions of a contract. Users of British Standards are responsible for their correct application. Compliance with a British Standard does not of itself confer immunity from legal obligations. Summary of pages This document comprises a front cover, an inside front cover, pages i and ii, pages 1 to 6, an inside back cover and a back cover. This standard has been updated (see copyright date) and may have had amendments incorporated. This will be indicated in the amendment table on the inside front cover. Licensed Copy: sheffieldun sheffieldun, na, Fri Dec 01 10:01:13 GMT+00:00 2006, Uncontrolled Copy, (c) BSI ISO 31-2:1992(E) © BSI 02-19991 Introduction 0.1 Arrangement of the tables The tables of quantities and units in ISO 31 are arranged so that the quantities are presented on the left-hand pages and the units on the corresponding right-hand pages. All units between two full lines belong to the quantities between the corresponding full lines on the left-hand pages. Where the numbering of an item has been changed in the revision of a part of ISO 31, the number in the preceding edition is shown in parentheses on the left-hand page under the new number for the quantity; a dash is used to indicate that the item in question did not appear in the preceding edition. 0.2 Tables of quantities The most important quantities within the field of this document are given together with their symbols and, in most cases, definitions. These definitions are given merely for identification; they are not intended to be complete. The vectorial character of some quantities is pointed out, especially when this is needed for the definitions, but no attempt is made to be complete or consistent. In most cases only one name and only one symbol for the quantity are given; where two or more names or two or more symbols are given for one quantity and no special distinction is made, they are on an equal footing. When two types of italic (sloping) letter exist (for example as with q, u; w, f; g, g) only one of these is given. This does not mean that the other is not equally acceptable. In general it is recommended that such variants should not be given different meanings. A symbol within parentheses implies that it is a “reserve symbol”, to be used when, in a particular context, the main symbol is in use with a different meaning. 0.3 Tables of units 0.3.1 General Units for the corresponding quantities are given together with the international symbols and the definitions. For further information, see ISO 31-0. The units are arranged in the following way: a) The names of the SI units are given in large print (larger than text size). The SI units have been adopted by the General Conference on Weights and Measures (Conference Générale des Poids et Mesures, CGPM). The SI units and their decimal multiples and sub-multiples are recommended, although the decimal multiples and sub-multiples are not explicitly mentioned. b) The names of non-SI units which may be used together with SI units because of their practical importance or because of their use in specialized fields are given in normal print (text size). These units are separated by a broken line from the SI units for the quantities concerned. c) The names of non-SI units which may be used temporarily together with SI units are given in small print (smaller than text size) in the “Conversion factors and remarks” column. d) The names of non-SI units which should not be combined with SI units are given only in annexes in some parts of ISO 31. These annexes are informative and not integral parts of the standard. They are arranged in three groups: 1) special names of units in the CGS system; 2) names of units based on the foot, pound and second and some other related units; 3) names of other units. 0.3.2 Remark on units for quantities of dimension one The coherent unit for any quantity of dimension one is the number one (1). When the value of such a quantity is expressed, the unit 1 is generally not written out explicitly. Prefixes shall not be used to form multiples or sub-multiples of this unit. Instead of prefixes, powers of 10 may be used. EXAMPLES Refractive index n = 1,53 × 1 = 1,53 Reynolds number Re = 1,32 × 103 Considering that plane angle is generally expressed as the ratio between two lengths, and solid angle as the ratio between an area and the square of a length, the CIPM specified in 1980 that, in the International System of Units, the radian and steradian are dimensionless derived units. This implies that the quantities plane angle and solid angle are considered as dimensionless derived quantities. The units radian and steradian may be used in expressions for derived units to facilitate distinction between quantities of different nature but having the same dimension. 0.4 Numerical statements All numbers in the “Definition” column are exact. When numbers in the “Conversion factors and remarks” column are exact, the word “exactly” is added in parentheses after the number. Licensed Copy: sheffieldun sheffieldun, na, Fri Dec 01 10:01:13 GMT+00:00 2006, Uncontrolled Copy, (c) BSI ISO 31-2:1992(E) 2 © BSI 02-1999 0.5 Special remark on logarithmic quantities and units The expression for the time dependence of a damped harmonic oscillation can be written either in real notation or as the real part of a complex notation This simple relation involving d and v can be obtained only when e (base of natural logarithms) is used as the base of the exponential function. The coherent SI unit for the damping coefficient d and the angular frequency v is second to the power minus one, 1/s. Using the special names neper, Np, and radian, rad, for the units of dt and vt respectively, the units for d and v become neper per second, Np/s, and radian per second, rad/s, respectively. Neper and radian are special names for the “dimensionless” unit one, 1. The neper is used as a unit for logarithmic quantities; the radian is used as a unit for plane angles and for the phase of circular functions. Corresponding variation in space is treated in the same manner where the unit for a is neper per metre, Np/m, and the unit for b is radian per metre, rad/m. In ISO 31, the level of a field quantity is therefore defined as the natural logarithm of a ratio of two amplitudes, LF = ln(F/F0), and is hence a quantity of dimension one. The unit neper (= the number 1) is the level of a field quantity when F/F0 = e. Since power is often proportional to the square of an amplitude, a factor 1/2 is introduced in the definition of the level of a power quantity LP (1/2) ln(P/P0) in order to make the level of the power quantity under these circumstances equal to the level of the field quantity. In practice the non-coherent unit degree, . °, (1° = p/180 rad) is often used for angles and the non-coherent unit bel, B, 1 B = (1/2) ln 10Np 1,151 293 Np based on common logarithms (base 10) for logarithmic quantities. Instead of the bel, its sub-multiple the decibel, dB, is commonly used. 1 Scope This part of ISO 31 gives names and symbols for quantities and units of periodic and related phenomena. Where appropriate, conversion factors are also given. 2 Normative reference The following standard contains provisions which, through reference in this text, constitute provisions of this part of ISO 31. At the time of publication, the edition indicated was valid. All standards are subject to revision, and parties to agreements based on this part of ISO 31 are encouraged to investigate the possibility of applying the most recent edition of the standard indicated below. Members of IEC and ISO maintain registers of currently valid International Standards. IEC 27-1:1971, Letter symbols to be used in electrical technology Part 1: General1). 3 Names and symbols The names and symbols for quantities and units of periodic and related phenomena are given on the following pages. 1) 5th edition, currently being revised. Licensed Copy: sheffieldun sheffieldun, na, Fri Dec 01 10:01:13 GMT+00:00 2006, Uncontrolled Copy, (c) BSI ISO 31-2:1992(E) © BSI 02-19993 PERIODIC AND RELATED PHENOMENAQuantities Item No.QuantitySymbolDefinitionRemarks 2-1period, periodic time TTime of one cycle 2-2time constant of an exponentially varying quantity Time after which the quantity would reach its limit if it maintained its initial rate of variation If a quantity is a function of time given by then is the time constant 2-3.1frequencyf, vf = 1/T 2-3.2rotational frequencynNumber of revolutions divided by time 2-4angular frequency, pulstance vv = 2pf 2-5wavelengthÆDistance in the direction of propagation of a periodic wave between two successive points where at a given time the phase is the same UnitsPERIODIC AND RELATED PHENOMENA Item No.Name of unitInternational symbol for unit DefinitionConversion factors and remarks 2-1.aseconds 2-2.aseconds 2-3.ahertzHz 1 Hz = 1 s1 1 Hz is the frequency of a periodic phenomenon of which the period is 1 s. 2-3.breciprocal second, second to the power minus one s1 The designations “revolutions per minute” (r/min) and “revolutions per second” (r/s) are widely used for rotating frequency in specifications on rotating machinery. Language-dependent abbreviations, such as the English rev/min and rpm (revolutions per second), and the French tr/min (tours par minute) and tr/s (tours par seconde), are not recommended.a a See also IEC 27-1. 2-4.aradian per secondrad/sSee the introduction, subclause 0.3.2. 2.4.breciprocal second, second to the power minus one s1 2-5.ametrem ångström (Å), 1 Å = 1010 m (exactly) Licensed Copy: sheffieldun sheffieldun, na, Fri Dec 01 10:01:13 GMT+00:00 2006, Uncontrolled Copy, (c) BSI ISO 31-2:1992(E) 4 © BSI 02-1999 PERIODIC AND RELATED PHENOMENAQuantities Item No.QuantitySymbolDefinitionRemarks 2-6repetency, wavenumber ss = 1/ÆThe vector quantities s s and k corresponding to repetency and angular repentency are called wave vector and propagation vector respectively. 2-7 (2-6.2) angular repetency, angular wavenumber kk = 2ps 2-8.1 () phase velocityc, v, cw, vw If velocities of electromagnetic waves and other velocities are both involved, then c should be used for the former and v for the latter. 2-8.2 () group velocitycg, vg 2-9 (2-7.1) level of a field quantity LFLF = ln(F/F0) where F and F0 represent two amplitudes of the same kind, F0 being a references amplitude If P/P0 = (F/F0)2 then LP = LF. Similar names, symbols and definitions apply to levels based on other quantities which are linear or quadratic functions of the amplitudes, respectively. The quantity on which the level is based should be specified in the name and by the subscript of the symbol, e.g. level of electric field strength LE. A difference between two field levels with the same reference F0 is called the field level difference DLF = ln(F1/F0) ln(F2/F0) = ln(F1/F2) independent of F0. An analogous relation applies to power level difference. 2-10 (2-8.1) level of a power quantity LP where P and P0 represent two powers, P0 being a reference power c v k -lf=