Standard measure There is one metric system, based on seven units and, yes, it is entirely consistent. By Stan Jakuba Downloaded from http://asmedigitalcollection.asme.org/memagazineselect/article-pdf/123/04/70/6382828/me-2001-apr6.pdf by guest on 25 September 2021 ,.. ,. 1110 • 110 ,ie ,;, ,ie ,,. ,;0 ,,. 200 210 220 2J) 2AO 200 200 ~ II1II 10 20 .. 10 *' eO to '10 '20 "" "" "" COMMON UNITS COMMON PREAXES THE MODERNIZED METRiC SYSTEM UnIt ~ ........ n. -modemlzlCf" metric tyswn aIM lntemllboNi SY*m NlST" 111 000000 cc ~ or SI (from N French "lA SyItetnI Cntema1ional ......-~- UA. ..... OII~ mill m 111000 d't.Jni\M.·whk;hil~ttldSl) . For~oflnt.mltioMI T..... ~ centime'o< " __ond __1hot ... ~by meIof ~ } ~ .,..,d e 11100 trade, .. metric aystem" mote than ~ St tt Inctudet the ,...NliUlfII...... T~ ___371 , 000 /t!stf5 ~ kilo k -" ~end~ttv~IheWOtld . for"~""""""'oI~ 1000000 U.l.ao..rr...,.....a.. kIog<om ~n ..... ... NOTE SeoIos ond_ .,. __10 (0) 'IfIIIqIDn. D.e 2CMOMJ2$ AIWId..-l883 iIM l ........ --gIgo G 1000000000 ,. 211 0"1 10 11 12 13 .. 11 17 11 20 21 22 23 XI 30 I I 'I' I I "I I I I I t f T I I I .S. ENGINEERS RARELY NEED one of the require­ est version, which is the practice with all standards. ments for their counterparts in most countries. The standard describes a universal, internationallan­ U They typically don't have to learn a second lan­ guage of measurement. guage. In most of the world, however, engineers are at Essentially, all units created in modern times are metric least bilingual. Most of them speak English. The arrangement may make it convenient for Ameri­ THE SEVEN METRIC BASE UNITS cans to ve nture abroad, but it also contributes to cultural isolation. And the isolation extends to the system of ~ Name ~ measurement. m meter length kg kilogram mass There have been an undue number ofletters to the ed­ s second time itor of this magazine over the years criticizing the metric K kelvin temperature system for its inconsistency (as compared to the English A ampere electric current mol mole amount of substance system, presumably). cd candela luminous intensity We little realize how inconsistent, illogical, and unsys­ tematic our own "system" is, because we are not readily confronted with al ternatives. DERIVED UNITS WITH SPECIAL NAMES The inconsistencies that critics of the metric system fo­ ~ Name ~ cus on are minuscule and most are due to the system's 8q becquerel radioactivity evolution. The evolution is inevitable. Any system that C coulomb electric charge wants to keep up with an evolving society must change. F farad capacitance Gy gray absorbed dose Among metric users, as in any population, there are H henry inductance people who do not want to accept change, or are not Hz hertz cycle frequency aware of revisions or the need for them, w ho prefer J joule energy to cling to established ways. Inconsistencies arise, then, kat katal molar flow Im lumen luminous flux in the way that people use the system, not in the sys­ Ix lux illuminance tem itself. N newton force There indeed is one, and only one, metric system­ W ohm resistance always the latest revision of the international standard Pa pascal pressure rad radian plane angle that describes it. For engineers worldwide, the standard S siemens conductance is ISO 1000. This standard is subject to change, as any sr steradian solid angle standard must be, and a user is expected to follow the lat- Sv sievert dose equivalent T tesla magnetic flux dens. V volt voltage (electric potency) Stan Jakuba is president of SI Jakub Associates in West W watt power HartJord, Conn., a firm that specializes in training and Wb weber magnetic flux consulting in metric standards. 70 APRIL 2001 MECHAN ICAL ENGINEER ING PHYSICAL QUANTITIES AND TYPICAL VALUES The author hopes that the article provided an understanding of the metric system. To get the feel of the units takes longer, and individual ini­ tiative is required. This table presents a sample of reference numbers for SI units that an engineer may need on a job. Looking at it for a few weeks helps in getting the feel for SI units-a feel of utmost importance in overcoming the resistance to using SI in one's work. Quantity Qld Units SI Unit Applications and Ballpark Figures Density (mass) Ib.jin.3, Ib.jft.3 kg/m3 Steel: 7,800 kg/m3; aluminum: 2,700 kg/m3; graphite: 1,700 kg/m3 Force ton, lb., oz. N M6 steel screw: 10 kN; a 102 kg man's gravity force: 1 kN on Earth Downloaded from http://asmedigitalcollection.asme.org/memagazineselect/article-pdf/123/04/70/6382828/me-2001-apr6.pdf by guest on 25 September 2021 Pressure psi, Ib.jft.2 Pa Car tire pressure: 200 kPa; screw steel: 800 MPa Modulus Ib.jft.2, Ib.jin.2 Pa Young's for steel: 200 GPa; for graphite: 120 MPa Heat content Btujlb. Jjkg Hydrogen LHV: 120 MJjkg Torque in.-Ib., ft.-lb. N·m M6 steel screw tightens to: 10 N·m Specific heat Btu/(Ib.-F) J/(kg.K) Aluminum: 0.9 kJ/(kg·K) Thermal conductivity Btu-ft.j(hr.-ft. 2-F) W/(m.K) Steel: 62 W/(m·K); concrete: 1 W/(m·K); aluminum alloys: 50 W/(m·K) Viscosity (kinematic) ft.2/hr. m2/ s Air: 15 mm2/ s; water: 1.1 mm2/s; fuel oil: 3.5 mm2/s Viscosity (dynamic) Ib.j(hr. -ft.) Pa·s Air: 18 mPa.s; water: 1.1 mPa·s; fuel oil: 2.9 mPa·s in every cou ntry of the world, including the United per mass or volume), the same logic leads to the units States. The evolution is coordinated by an international Jlkg or Jlm 3. committee in which the United States has participated Many derived units can be expressed in more than one since 1875. form, but professional use usually settles on a single con­ It may be comforting to many to learn that the stan­ vention. For example, the unit of dynamic viscosity dard, in the section most people use, is not expected to could be expressed as kg/(n1'S) or N'm2 or Pa·s. Only the change for a long time. And the last major revision took last form is prevalent. place in 1960-two generations ago. Note that there is no officially recognized forum for HOLDOVERS FROM THE PAST the developnlent of any other system of units, including As pointed out in the letters to the editors, there are the English system or any version of it'. inconsistencies in the sense that non-SI units and terms The modern system of measurement is properly called remain in local (and, in some cases, general and ap­ SI, not metric. SI, for the French Syste1l1e International, is proved) use. They mostly reflect a tradition that is slow built on seven arbitrary units, called base units. Individu­ to die. ally, they measure such basic physical quantities as length, Here are several examples of terms carried over from. mass, or time. Alone or in combination, they let man­ the past that are still in common and approved use. kind measure anything. The degree Celsius (symbol °C) is an alternate name for the kelvin when a temperature increment is meant. It DERIVED UNITS is also a name that designates a temperature on the Cel­ There are, of course, hundreds of units needed for mea­ sius scale. suring "anything," but they are all derived from those The degree in plane angle (symbol 0) is an alternative to seven. The derivation is done in a way that provides the the SI radian. marvelous and unique feature of SI: There are no con­ The liter and milliliter are the everyday usage alternates version factors. for dm3 and cm3, respectively. Some of the derivations were given a special name. Prefixes (for example, kilo-, centi-, and milli-) often This was done in cases where the combination would be too long and cumbersome for frequent use, or where confusion could result. Most have been used in the Eng­ COMMON PREFIXES AND THEIR MEANINGS lish system for generations because no official non­ metric equivalent ever existed. Prefix Symbol Meaning All derived units can be expressed in terms of the base GIGA G billion (U .S.) units. For example, the SI unit for force, called the new­ MEGA M million KILO k thousand ton, is derived from mass times acceleration, the kilo­ HEKTO h hundred gram accelerating a meter per second per second or, in DEKA da ten graphic symbols, kg'm/s2 DECI d tenth Most derived units are as straightforward as the rela­ CENTI c hundredth MILLI m thousandth 2 tionship of length to breadth to compute area, m . MICRO 11 millionth Knowing that torque means force times distance leads to NANO n billionth the newton meter, N·m. Or, for energy density (energy Seven Units, Defined by Their Keepers MECHANICAL ENGINEERING cribbed the definitions of the the radiation corresponding to the transition between seven metric base units from the Web site of the National the two hyperfine levels of the ground state of the cesium Institute of Standards and Technology, http://physics. 133 atom." nist.gov/cuu/ Units/current.html. "The ampere is that constant current which, if maintained The text of the definitions is the same, word for word, as in two straight parallel conductors of infinite length, of neg­ that published on the English-language Web site of the Bu­ ligible circular cross-section, and placed 1 meter apart in reau International des Poids et Mesures, the international vacuum, would produce between these conductors a force standards body, www.bipm.org/enus/3_Sljbase_units.