Standard measure There is one , 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

.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 lan­ guage of . 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 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 temperature system for its inconsistency (as compared to the English A electric current mol amount of substance system, presumably). cd 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 radioactivity evolution. The evolution is inevitable. Any system that C electric charge wants to keep up with an evolving society must change. F capacitance Gy absorbed dose Among metric users, as in any population, there are H inductance people who do not want to accept change, or are not Hz cycle frequency aware of revisions or the need for them, w ho prefer J energy to cling to established ways. Inconsistencies arise, then, kat katal molar flow Im luminous flux in the way that people use the system, not in the sys­ Ix illuminance tem itself. N force There indeed is one, and only one, metric system­ W resistance always the latest revision of the international standard Pa pressure rad plane angle that describes it. For engineers worldwide, the standard S conductance is ISO 1000. This standard is subject to change, as any sr solid angle standard must be, and a user is expected to follow the lat- Sv dose equivalent T magnetic flux dens. V voltage (electric potency) Stan Jakuba is president of SI Jakub Associates in West W power HartJord, Conn., a firm that specializes in training and Wb 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 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 (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. equal to 2 x 10-7 newton per meter of length."

html. "The kelvin, unit of thermodynamic temperature, is the Downloaded from http://asmedigitalcollection.asme.org/memagazineselect/article-pdf/123/04/70/6382828/me-2001-apr6.pdf by guest on 25 September 2021 "The meter is the length of the path traveled by light fraction 1/273.16 of the thermodynamic temperature of in vacuum during a time interval of 1/299 792 458 of the triple point of water." a second." "The mole is the amount of substance of a system which "The kilogram is the unit of mass; it is equal to the mass contains as many elementary entities as there are atoms in of the international prototype of the kilogram." 0.012 kilogram of carbon 12; its symbol is 'mol.' When the [Another NIST document says: "The standard for the unit mole is used, the elementary entities must be specified and of mass, the kilogram, is a cylinder of platinum-iridium al­ may be atoms, molecules, ions, electrons, other particles, loy kept by the International Bureau of Weights and Mea­ or specified groups of such particles." sures near Paris. A duplicate in the custody of the National "The candela is the luminous intensity, in a given direc­ Institute of Standards and Technology serves as the mass tion, of a source that emits monochromatic radiation of fre­ standard for the United States. This is the only base unit quency 540 x 1012 hertz and that has a radiant intensity in still defined by artifact.'1 that direction of 1/683 watt per steradian." "The second is the duration of 9 192 631 770 periods of -The Editors

precede the name of a unit. Pre­ fixes, far fewer-perhaps eight­ fixes were devised to simplify, are needed in daily life and in like the familiar 10n notation common technical work. (for example, 50,000 expressed Ten are more than most peo­ as 5xl 04). The prefixes also avoid ple need. the creation of unnecessary new units, like 5,280 feet grouped GETTING TO LIKE SI into one mile. Most people, once they under­ The 10n notation is impractical stand it, like SI for its logic, con­ for the non-scientific person, and sistency, and lack of conversion the creation of new units is im­ factors. On the other hand, some practical for everybody, because in older U.S. engineers don't like to the modern world it would ne­ use it. This is understandable. cessitate coining thousands of One dislikes anything that one names and subjecting each of us does not understand and has little to memorizing hundreds of them. feel for. Instead, the prefixes shorten For technical documentation, long numbers to make them con­ the preferred way of writing SI venient for everybody to use. prefixes and units is by their sym­ With a rare exception, Ameri­ bols; for example, 5 kg, not 5 can students consider km. and kilogram or five . mm two separate units. That The kilogram, with a cylinder of platinum-iridium alloy as its SI units, prefixes, and rules were standard. is the only SI base unit still defined by an artifact. misconception trails through the established to fac ilitate data com- college years among all but the most astute students and munication worldwide. They represent a compromise is a leading argument against metric for having "too intended to suit all languages, to ease arithmetic manip­ many and long-named units." Of course, km or mm is a ulations, to prevent ambiguity, and to retain some of the way of saying in shorthand "a thousand meters" or "a tradition of the metric system. thousandth of a meter." They are just multiples of units. If each symbol is written according to the SI rules­ We seem to be able to treat "kilobyte," "megabyte," and distinguishing between uppercase and lowercase letters, "gigabyte" quite comfortably. This author has not heard and between the Latin and Greek letters-it will be in­ as yet anyone claiming them to be three different units. telligible anywhere, regardless of the script and language While the SI committee has so far established 20 pre- a nation uses . _

72 API'l.. IL 200 1 M EC H AN IC AL E NG INEERI NG