402:
38:
2361:
1051:
is commonly used in fluid mechanics to characterize flow, incorporating both properties of the fluid and the flow. It is interpreted as the ratio of inertial forces to viscous forces and can indicate flow regime as well as correlate to frictional heating in application to flow in
783:
may be defined as a ratio of volumes (volumetric moisture, m⋅m, dimension L⋅L) or as a ratio of masses (gravimetric moisture, units kg⋅kg, dimension M⋅M); both would be unitless quantities, but of different dimension.
1045:– defined as the ratio of momentum diffusivity (kinematic viscosity) and mass diffusivity, and is used to characterize fluid flows in which there are simultaneous momentum and mass diffusion convection processes.
1479:
474:– they are inversely proportional). If the dimensionless combinations' values changed with the systems of units, then the equation would not be an identity, and Buckingham's theorem would not hold.
1751:
1452:
854:
can be normalized in this fashion. For example, the values of the following constants are independent of the system of units, cannot be defined, and can only be determined experimentally:
959:
466:
theorem indicates that validity of the laws of physics does not depend on a specific unit system. A statement of this theorem is that any physical law can be expressed as an
1113:
1179:
1146:
985:– parameter used in the context of special relativity for time dilation, length contraction, and relativistic effects between observers moving at different velocities
1080:
652:
of quantities that are not dimensionless, but whose dimensions cancel out in the mathematical operation. Examples of quotients of dimension one include calculating
1082:, is the ratio of the heat release rate of a fire to the enthalpy of the gas flow rate circulating through the fire. Accidental and natural fires usually have a
1039:) is a dimensionless number used in mass-transfer operation. It represents the ratio of the convective mass transfer to the rate of diffusive mass transport.
355:
as a physical unit. The idea was rebutted on the grounds that such a change would raise inconsistencies for both established dimensionless groups, like the
2347:
1694:
1017:(Da) – used in chemical engineering to relate the chemical reaction timescale (reaction rate) to the transport phenomena rate occurring in a system.
372:
219:, the use of dimensionless parameters is evident in geometric relationships and transformations. Physics relies on dimensionless numbers like the
2274:
1335:
240:
470:
involving only dimensionless combinations (ratios or products) of the variables linked by the law (e. g., pressure and volume are linked by
1360:
576:
may represent dimensionless quantities. They can represent discrete quantities, which can also be dimensionless. More specifically,
102:
1695:"Lost dimension: A flaw in the SI system leaves physicists grappling with ambiguous units - SI units need reform to avoid confusion"
1002:
343:
There have been periodic proposals to "patch" the SI system to reduce confusion regarding physical dimensions. For example, a 2017
74:
423:
55:
2365:
1023:– describes the relationship between diffusion and reaction rate in porous catalyst pellets with no mass transfer limitations.
81:
2085:
2028:
1987:
1489:
1462:
304:
contributed to the understanding of dimensionless numbers in physics. Building on
Rayleigh's method of dimensional analysis,
1869:
1838:
672:
such as ppm (= 10), ppb (= 10), and ppt (= 10), or perhaps confusingly as ratios of two identical units (
88:
2381:
1644:
449:
121:
2106:
Johansson, Ingvar (2010). "Metrological thinking needs the notions of parametric quantities, units and dimensions".
431:
1319:
1266:
971:
803:
70:
1011:– ratio of plasma pressure to magnetic pressure, used in magnetospheric physics as well as fusion plasma physics.
793:
427:
59:
2215:
1294:
888:
17:
322:
Numerous dimensionless numbers, mostly ratios, were coined in the early 1900s, particularly in the areas of
1505:
Webb, J. K.; King, J. A.; Murphy, M. T.; Flambaum, V. V.; Carswell, R. F.; Bainbridge, M. B. (2011-10-31).
516:. For the purposes of the experimenter, different systems that share the same description by dimensionless
874:
1250:
is the measurement of the proportional change of an economic variable in response to a change in another
1979:
1281:
1148:. Fires originating from pressured vessels or pipes, with additional momentum caused by pressure, have
560:
2245:
2219:
1776:
1253:
929:
661:
1085:
95:
724:
412:
267:
177:
1904:
1376:
866:
416:
228:
48:
1151:
1118:
861:, a measure of physical deformation defined as a change in length divided by the initial length.
391:
309:
1256:
is a dimensionless ratio used in epidemiology to quantify the transmissibility of an infection.
1247:
1219:
736:
486:
478:
467:
2053:
1973:
2283:
2184:
2014:
1563:
1332:
International vocabulary of metrology — Basic and general concepts and associated terms (VIM)
1008:
216:
208:
200:
2296:
2117:
1943:
1711:
1658:
1528:
1417:
1380:
1276:
1224:
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494:
277:
1506:
1014:
8:
1285:
904:
657:
597:
285:
255:
150:
142:
2300:
2121:
1947:
1715:
1662:
1594:
1532:
1421:
2333:
2312:
2278:
2141:
1820:
1743:
1518:
1299:
1026:
858:
815:
728:
689:
669:
633:
293:
149:
that align with another system, these quantities do not necessitate explicitly defined
138:
2308:
2077:
997:– ratio of the speed of an object or flow relative to the speed of sound in the fluid.
2338:
2320:
2145:
2133:
2129:
2024:
2010:
1983:
1912:
1812:
1804:
1735:
1727:
1622:
1614:
1544:
1485:
1458:
1433:
1429:
1237:
851:
681:
248:
232:
154:
1824:
1356:
359:, and for mathematically distinct entities that happen to have the same units, like
2328:
2304:
2196:
2159:
2125:
2020:
1951:
1900:
1794:
1785:
1747:
1719:
1702:
1674:
1666:
1640:
1606:
1575:
1540:
1536:
1425:
1206:
1029:– characterizes the range of angles over which the system can accept or emit light.
811:
780:
740:
577:
348:
305:
297:
158:
1932:"On Physically Similar Systems; Illustrations of the Use of Dimensional Equations"
1645:"On physically similar systems; illustrations of the use of dimensional equations"
1969:
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1610:
1048:
1032:
839:
831:
807:
637:
625:
601:
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323:
316:
220:
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1845:
1405:
2163:
2016:
Development of
Mathematical Cognition: Neural Substrates and Genetic Influences
1271:
1194:
1042:
1036:
1020:
988:
982:
799:
632:
is a related concept in statistics. The concept may be generalized by allowing
621:
612:
471:
331:
281:
236:
224:
162:
1679:
2375:
2324:
2316:
2292:
2137:
1808:
1731:
1618:
1437:
1184:
843:
665:
565:
364:
327:
301:
252:
2279:"Redressing grievances with the treatment of dimensionless quantities in SI"
276:, regularly occur in sciences, and are formally treated within the field of
2342:
2200:
1931:
1916:
1816:
1739:
1626:
1579:
1548:
910:
847:
708:
1955:
1670:
1595:"Dimensionless Equation of State to Predict Microemulsion Phase Behavior"
1454:
A History of the Circle: Mathematical
Reasoning and the Physical Universe
1189:
994:
923:
835:
677:
606:
593:
368:
1905:"An ontology on property for physical, chemical, and biological systems"
2108:
1385:
1289:
1241:
760:
having equal dimensions in numerator and denominator are actually only
720:
629:
376:
212:
166:
616:
is a related linguistics concept. Counting numbers, such as number of
892:
716:
497:
379:", but the idea of just introducing a new SI name for 1 was dropped.
289:
244:
196:
1799:
1780:
1723:
401:
37:
1507:"Indications of a Spatial Variation of the Fine Structure Constant"
900:
673:
553:
517:
513:
204:
2223:
1523:
2185:"Zur Elektrodynamik bewegter Körper [AdP 17, 891 (1905)]"
1564:"Zur Elektrodynamik bewegter Körper [AdP 17, 891 (1905)]"
732:
704:
685:
548:
337:
2216:"NRL Plasma Formulary: Dimensionless Numbers of Fluid Mechanics"
2360:
1481:
EBOOK: Fluid
Mechanics Fundamentals and Applications (SI units)
896:
823:
712:
360:
352:
319:'s previous work) to formalize the nature of these quantities.
189:
181:
798:
Certain universal dimensioned physical constants, such as the
604:. In mathematics, the "number of elements" in a set is termed
2054:"ISO 80000-1:2022(en) Quantities and units — Part 1: General"
1357:"SI Brochure: The International System of Units, 9th Edition"
1210:
653:
649:
344:
185:
146:
1870:"BIPM Consultative Committee for Units (CCU), 16th Meeting"
1839:"BIPM Consultative Committee for Units (CCU), 15th Meeting"
827:
819:
719:
are defined as ratios of quantities of the same kind. In
617:
195:
Dimensionless quantities play a crucial role serving as
700:
288:
led significant developments in the modern concepts of
1504:
932:
1154:
1121:
1088:
1061:
746:
It has been argued that quantities defined as ratios
173:
926:
ratio of the mass of any given elementary particle,
1593:Ghosh, Soumyadeep; Johns, Russell T. (2016-09-06).
787:
188:, derived from the universal ratio of 2π times the
62:. Unsourced material may be challenged and removed.
1173:
1140:
1107:
1074:
953:
643:
873:≈ 1/137 which characterizes the magnitude of the
141:in a manner that prevents their aggregation into
137:, or quantities of dimension one, are quantities
2373:
2008:
818:can be normalized to 1 if appropriate units for
373:International Committee for Weights and Measures
161:; its value remains independent of the specific
846:, specifically regarding these five constants,
707: (= 0.001). Some angle units such as
636:to account for fractions of a full item, e.g.,
477:Another consequence of the theorem is that the
371:). In another instance in the early 2000s, the
2275:National Institute of Standards and Technology
2048:
2046:
1115:. Flat spread fires such as forest fires have
500:occurring in those variables to give a set of
192:of a circle being equal to its circumference.
2099:
1962:
1477:
991:– wavenumber(spatial frequency) over distance
764:and still have physical dimension defined as
620:, can be compounded with units of frequency (
1374:
903:. An analogous ratio can be defined for any
648:Dimensionless quantities can be obtained as
280:. In the 19th century, French mathematician
2273:Flater, David (October 2017) . Written at
2164:"How Many Fundamental Constants Are There?"
2043:
1687:
1478:Cengel, Yunus; Cimbala, John (2013-10-16).
684:, which characterizes the concentration of
430:. Unsourced material may be challenged and
215:often involve dimensionless quantities. In
1978:. Key Topics in Semantics and Pragmatics.
1929:
1769:
1639:
1592:
1349:
976:
481:dependence between a certain number (say,
2332:
2105:
1968:
1798:
1678:
1522:
1450:
699:Other common proportions are percentages
624:) to derive units of count rate, such as
450:Learn how and when to remove this message
122:Learn how and when to remove this message
2182:
1561:
1003:Dimensionless numbers in fluid mechanics
584:. The concept is formalized as quantity
2243:
1781:"Don't tamper with SI-unit consistency"
385:
375:discussed naming the unit of 1 as the "
315:(independently of French mathematician
207:, concepts like the unitless ratios in
14:
2374:
2272:
1899:
2246:"Fluid Dynamic Aspects of Room Fires"
2086:Massachusetts Institute of Technology
1775:
1403:
203:in various technical disciplines. In
2213:
2158:
1975:Semantics for Counting and Measuring
428:adding citations to reliable sources
395:
340:(dB) finds widespread use nowadays.
60:adding citations to reliable sources
31:
2052:
1244:in moving from one place to another
489:can be reduced by the number (say,
330:. Measuring logarithm of ratios as
296:. Later work by British physicists
268:Dimensional analysis § History
27:Quantity with no physical dimension
24:
2266:
1844:. 17–18 April 2003. Archived from
1227:(which is sometimes dimensionless)
25:
2393:
2353:
2309:10.1016/j.measurement.2017.05.043
1035:– (also called the mass transfer
272:Quantities having dimension one,
184:serve as dimensionless units for
176:is recognized as a dimensionless
2359:
2222:. pp. 23–25. Archived from
2013:; Koepke, Kathleen Mann (2015).
1267:List of dimensionless quantities
972:List of dimensionless quantities
954:{\textstyle {\sqrt {\hbar c/G}}}
804:universal gravitational constant
788:Dimensionless physical constants
400:
36:
2277:, Gaithersburg, Maryland, USA.
2237:
2207:
2176:
2152:
2070:
2002:
1923:
1893:
1862:
1831:
1757:from the original on 2022-12-21
1633:
1381:"Dimensionless units in the SI"
1231:
794:Dimensionless physical constant
644:Ratios, proportions, and angles
47:needs additional citations for
1586:
1555:
1541:10.1103/PhysRevLett.107.191101
1498:
1471:
1444:
1397:
1368:
1312:
1108:{\displaystyle Q^{*}\approx 1}
1055:Zukoski number, usually noted
13:
1:
1305:
1295:Orders of magnitude (numbers)
889:proton-to-electron mass ratio
660:. Another set of examples is
1611:10.1021/acs.langmuir.6b02666
1457:. Rutgers University Press.
1288:, the analogous concepts in
1200:
7:
2244:Zukoski, Edward E. (1986).
2183:Einstein, A. (2005-02-23).
1562:Einstein, A. (2005-02-23).
1260:
875:electromagnetic interaction
735:and is used to measure the
703: (= 0.01),
523:
512:independent, dimensionless
351:argued for formalizing the
10:
2398:
2130:10.1088/0026-1394/47/3/012
2078:"7.3 Dimensionless groups"
1980:Cambridge University Press
1777:Wendl, Michael Christopher
1451:Zebrowski, Ernest (1999).
1430:10.1088/0026-1394/31/6/013
1282:Normalization (statistics)
1174:{\displaystyle Q^{*}\gg 1}
1141:{\displaystyle Q^{*}<1}
1000:
969:
838:are chosen. The resulting
791:
389:
265:
261:
2220:Naval Research Laboratory
1710:(7666): 135. 2017-08-10.
1700:. This Week: Editorials.
1404:Mills, I. M. (May 1995).
1326:quantity of dimension one
1254:Basic reproduction number
559:
547:
535:
530:
145:. Typically expressed as
2382:Dimensionless quantities
2214:Huba, Joseph D. (2007).
1377:Phillips, William Daniel
725:coefficient of variation
274:dimensionless quantities
169:per milliliter (mL/mL).
135:Dimensionless quantities
71:"Dimensionless quantity"
1930:Buckingham, E. (1914).
1511:Physical Review Letters
1365:ISBN 978-92-822-2272-0.
1328:dimensionless quantity"
977:Physics and engineering
965:
899:divided by that of the
867:fine-structure constant
658:unit conversion factors
580:can be used to express
284:and Scottish physicist
229:fine-structure constant
2201:10.1002/andp.200590006
1580:10.1002/andp.200590006
1220:Standard atomic weight
1209:– density relative to
1175:
1142:
1109:
1076:
955:
692:, could be written as
668:, often written using
336:in the (derived) unit
201:differential equations
2366:Dimensionless numbers
2251:. Fire Safety Science
1956:10.1103/physrev.4.345
1671:10.1103/PhysRev.4.345
1176:
1143:
1110:
1077:
1075:{\displaystyle Q^{*}}
1009:Beta (plasma physics)
1001:Further information:
956:
217:differential geometry
2368:at Wikimedia Commons
1277:Dimensional analysis
1225:Equilibrium constant
1216:Relative atomic mass
1152:
1119:
1086:
1059:
930:
891:. This ratio is the
727:is the ratio of the
680:/mol). For example,
582:countable quantities
424:improve this section
392:Buckingham π theorem
386:Buckingham π theorem
278:dimensional analysis
256:concentration ratios
186:angular measurements
143:units of measurement
56:improve this article
2301:2017Meas..109..105F
2122:2010Metro..47..219J
1948:1914PhRv....4..345B
1716:2017Natur.548R.135.
1663:1914PhRv....4..345B
1533:2011PhRvL.107s1101W
1422:1995Metro..31..537M
1286:standardized moment
905:elementary particle
850:. However, not all
762:unitless quantities
640:equal to one half.
634:non-integer numbers
598:number of particles
596:. Examples include
367:) versus energy (a
286:James Clerk Maxwell
258:are dimensionless.
251:and ratios such as
157:(ABV) represents a
2189:Annalen der Physik
2011:Geary, David Cyril
2009:Berch, Daniel B.;
1779:(September 2017).
1680:10338.dmlcz/101743
1568:Annalen der Physik
1300:Similitude (model)
1171:
1138:
1105:
1072:
1027:Numerical aperture
951:
913:coupling strength
877:between electrons.
859:engineering strain
852:physical constants
816:Boltzmann constant
729:standard deviation
690:alcoholic beverage
670:parts-per notation
586:number of entities
531:Number of entities
139:implicitly defined
2364:Media related to
2160:Baez, John Carlos
2030:978-0-12-801909-2
1989:978-1-107-00127-5
1641:Buckingham, Edgar
1605:(35): 8969–8979.
1491:978-0-07-717359-3
1464:978-0-8135-2898-4
1406:"Unity as a Unit"
1238:Cost of transport
1015:Damköhler numbers
949:
682:alcohol by volume
571:
570:
460:
459:
452:
233:quantum mechanics
165:used, such as in
155:alcohol by volume
132:
131:
124:
106:
16:(Redirected from
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2021:Elsevier Science
2006:
2000:
1999:
1997:
1996:
1970:Rothstein, Susan
1966:
1960:
1959:
1927:
1921:
1920:
1897:
1891:
1890:
1888:
1887:
1881:
1875:. Archived from
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1866:
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1850:
1843:
1835:
1829:
1828:
1802:
1773:
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1441:
1401:
1395:
1394:
1375:Mohr, Peter J.;
1372:
1366:
1364:
1353:
1347:
1346:
1344:
1343:
1316:
1207:Relative density
1180:
1178:
1177:
1172:
1164:
1163:
1147:
1145:
1144:
1139:
1131:
1130:
1114:
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1111:
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1081:
1079:
1078:
1073:
1071:
1070:
960:
958:
957:
952:
950:
945:
934:
842:is known as the
812:Coulomb constant
781:moisture content
778:
759:
695:
578:counting numbers
528:
527:
520:are equivalent.
465:
455:
448:
444:
441:
435:
404:
396:
312:
306:Edgar Buckingham
298:Osborne Reynolds
249:state properties
159:volumetric ratio
153:. For instance,
127:
120:
116:
113:
107:
105:
64:
40:
32:
21:
2397:
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2392:
2391:
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2388:
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2372:
2371:
2356:
2345:. NIHMS1633436.
2269:
2267:Further reading
2264:
2263:
2254:
2252:
2248:
2242:
2238:
2229:
2227:
2212:
2208:
2195:(S1): 194–224.
2181:
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2100:
2091:
2089:
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2062:
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2051:
2044:
2035:
2033:
2031:
2007:
2003:
1994:
1992:
1990:
1982:. p. 206.
1967:
1963:
1936:Physical Review
1928:
1924:
1898:
1894:
1885:
1883:
1879:
1872:
1868:
1867:
1863:
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1852:
1848:
1841:
1837:
1836:
1832:
1800:10.1038/549160d
1774:
1770:
1760:
1758:
1754:
1724:10.1038/548135b
1697:
1693:
1692:
1688:
1650:Physical Review
1638:
1634:
1591:
1587:
1574:(S1): 194–224.
1560:
1556:
1503:
1499:
1492:
1484:. McGraw Hill.
1476:
1472:
1465:
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1445:
1402:
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1234:
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1155:
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1149:
1126:
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1120:
1117:
1116:
1093:
1089:
1087:
1084:
1083:
1066:
1062:
1060:
1057:
1056:
1049:Reynolds number
1033:Sherwood number
1005:
979:
974:
968:
941:
933:
931:
928:
927:
919:
840:system of units
808:Planck constant
802:in vacuum, the
796:
790:
779:. For example,
765:
747:
693:
646:
638:number of turns
626:bits per second
613:Countable nouns
602:population size
574:Integer numbers
538:
526:
463:
462:The Buckingham
456:
445:
439:
436:
421:
405:
394:
388:
382:
357:Strouhal number
324:fluid mechanics
317:Joseph Bertrand
310:
270:
264:
221:Reynolds number
163:units of volume
128:
117:
111:
108:
65:
63:
53:
41:
28:
23:
22:
15:
12:
11:
5:
2395:
2385:
2384:
2370:
2369:
2355:
2354:External links
2352:
2351:
2350:
2291:. London, UK:
2268:
2265:
2262:
2261:
2236:
2206:
2175:
2162:(2011-04-22).
2151:
2116:(3): 219–230.
2098:
2069:
2042:
2029:
2023:. p. 13.
2001:
1988:
1961:
1942:(4): 345–376.
1922:
1911:(117): 1–210.
1892:
1861:
1830:
1768:
1686:
1657:(4): 345–376.
1632:
1585:
1554:
1517:(19): 191101.
1497:
1490:
1470:
1463:
1443:
1416:(6): 537–541.
1396:
1379:(2015-06-01).
1367:
1348:
1310:
1309:
1307:
1304:
1303:
1302:
1297:
1292:
1279:
1274:
1272:Arbitrary unit
1269:
1262:
1259:
1258:
1257:
1251:
1245:
1233:
1230:
1229:
1228:
1222:
1213:
1202:
1199:
1198:
1197:
1195:Grashof number
1192:
1187:
1182:
1170:
1167:
1162:
1158:
1137:
1134:
1129:
1125:
1104:
1101:
1096:
1092:
1069:
1065:
1053:
1046:
1043:Schmidt number
1040:
1037:Nusselt number
1030:
1024:
1021:Thiele modulus
1018:
1012:
999:
998:
992:
989:Fresnel number
986:
983:Lorentz Factor
978:
975:
970:Main article:
967:
964:
963:
962:
948:
944:
940:
937:
921:
917:
908:
887:) ≈ 1836, the
878:
863:
862:
800:speed of light
792:Main article:
789:
786:
666:mole fractions
662:mass fractions
645:
642:
622:inverse second
569:
568:
563:
557:
556:
551:
545:
544:
539:
537:Common symbols
536:
533:
532:
525:
522:
458:
457:
408:
406:
399:
390:Main article:
387:
384:
369:scalar product
365:vector product
282:Joseph Fourier
263:
260:
253:mole fractions
237:Lorentz factor
225:fluid dynamics
130:
129:
44:
42:
35:
26:
9:
6:
4:
3:
2:
2394:
2383:
2380:
2379:
2377:
2367:
2362:
2358:
2357:
2348:
2344:
2340:
2335:
2330:
2326:
2322:
2318:
2314:
2310:
2306:
2302:
2298:
2294:
2293:Elsevier Ltd.
2290:
2286:
2285:
2280:
2276:
2271:
2270:
2247:
2240:
2226:on 2021-04-27
2225:
2221:
2217:
2210:
2202:
2198:
2194:
2190:
2186:
2179:
2165:
2161:
2155:
2147:
2143:
2139:
2135:
2131:
2127:
2123:
2119:
2115:
2111:
2110:
2102:
2088:
2087:
2079:
2073:
2059:
2055:
2049:
2047:
2032:
2026:
2022:
2018:
2017:
2012:
2005:
1991:
1985:
1981:
1977:
1976:
1971:
1965:
1957:
1953:
1949:
1945:
1941:
1937:
1933:
1926:
1918:
1914:
1910:
1906:
1902:
1896:
1882:on 2006-11-30
1878:
1871:
1865:
1851:on 2006-11-30
1847:
1840:
1834:
1826:
1822:
1818:
1814:
1810:
1806:
1801:
1796:
1793:(7671): 160.
1792:
1788:
1787:
1782:
1778:
1772:
1753:
1749:
1745:
1741:
1737:
1733:
1729:
1725:
1721:
1717:
1713:
1709:
1705:
1704:
1696:
1690:
1681:
1676:
1672:
1668:
1664:
1660:
1656:
1652:
1651:
1646:
1642:
1636:
1628:
1624:
1620:
1616:
1612:
1608:
1604:
1600:
1596:
1589:
1581:
1577:
1573:
1569:
1565:
1558:
1550:
1546:
1542:
1538:
1534:
1530:
1525:
1520:
1516:
1512:
1508:
1501:
1493:
1487:
1483:
1482:
1474:
1466:
1460:
1456:
1455:
1447:
1439:
1435:
1431:
1427:
1423:
1419:
1415:
1411:
1407:
1400:
1392:
1388:
1387:
1382:
1378:
1371:
1362:
1358:
1352:
1337:
1333:
1329:
1327:
1323:
1315:
1311:
1301:
1298:
1296:
1293:
1291:
1287:
1283:
1280:
1278:
1275:
1273:
1270:
1268:
1265:
1264:
1255:
1252:
1249:
1246:
1243:
1239:
1236:
1235:
1226:
1223:
1221:
1217:
1214:
1212:
1208:
1205:
1204:
1196:
1193:
1191:
1188:
1186:
1185:Eckert number
1183:
1168:
1165:
1160:
1156:
1135:
1132:
1127:
1123:
1102:
1099:
1094:
1090:
1067:
1063:
1054:
1050:
1047:
1044:
1041:
1038:
1034:
1031:
1028:
1025:
1022:
1019:
1016:
1013:
1010:
1007:
1006:
1004:
996:
993:
990:
987:
984:
981:
980:
973:
946:
942:
938:
935:
925:
922:
916:
912:
909:
906:
902:
898:
894:
890:
886:
882:
879:
876:
872:
868:
865:
864:
860:
857:
856:
855:
853:
849:
845:
844:natural units
841:
837:
833:
829:
825:
821:
817:
813:
809:
805:
801:
795:
785:
782:
777:
773:
769:
763:
758:
754:
750:
744:
742:
738:
734:
730:
726:
722:
718:
714:
710:
706:
702:
697:
691:
687:
683:
679:
675:
671:
667:
663:
659:
655:
651:
641:
639:
635:
631:
627:
623:
619:
615:
614:
609:
608:
603:
599:
595:
591:
587:
583:
579:
575:
567:
564:
562:
558:
555:
552:
550:
546:
543:
540:
534:
529:
521:
519:
515:
511:
507:
503:
499:
496:
492:
488:
484:
480:
475:
473:
469:
454:
451:
443:
433:
429:
425:
419:
418:
414:
409:This section
407:
403:
398:
397:
393:
383:
380:
378:
374:
370:
366:
362:
358:
354:
350:
346:
341:
339:
335:
334:
329:
328:heat transfer
325:
320:
318:
314:
307:
303:
302:Lord Rayleigh
299:
295:
291:
287:
283:
279:
275:
269:
259:
257:
254:
250:
246:
242:
238:
234:
230:
226:
222:
218:
214:
210:
206:
202:
198:
193:
191:
187:
183:
179:
178:base quantity
175:
170:
168:
164:
160:
156:
152:
148:
144:
140:
136:
126:
123:
115:
104:
101:
97:
94:
90:
87:
83:
80:
76:
73: –
72:
68:
67:Find sources:
61:
57:
51:
50:
45:This article
43:
39:
34:
33:
30:
19:
18:Dimensionless
2288:
2282:
2253:. Retrieved
2239:
2228:. Retrieved
2224:the original
2209:
2192:
2188:
2178:
2167:. Retrieved
2154:
2113:
2107:
2101:
2090:. Retrieved
2084:
2072:
2061:. Retrieved
2057:
2034:. Retrieved
2015:
2004:
1993:. Retrieved
1974:
1964:
1939:
1935:
1925:
1909:APMIS Suppl.
1908:
1901:Dybkær, René
1895:
1884:. Retrieved
1877:the original
1864:
1853:. Retrieved
1846:the original
1833:
1790:
1784:
1771:
1759:. Retrieved
1707:
1701:
1689:
1654:
1648:
1635:
1602:
1598:
1588:
1571:
1567:
1557:
1514:
1510:
1500:
1480:
1473:
1453:
1446:
1413:
1409:
1399:
1390:
1384:
1370:
1351:
1340:. Retrieved
1331:
1325:
1321:
1314:
1232:Other fields
914:
911:Strong force
884:
880:
870:
848:Planck units
797:
775:
771:
767:
761:
756:
752:
748:
745:
698:
647:
611:
605:
589:
585:
581:
572:
549:SI unit
541:
509:
505:
501:
490:
482:
476:
461:
446:
437:
422:Please help
410:
381:
342:
332:
321:
273:
271:
194:
171:
134:
133:
118:
109:
99:
92:
85:
78:
66:
54:Please help
49:verification
46:
29:
2295:: 105–110.
2284:Measurement
1190:Biot number
995:Mach number
924:Planck mass
836:temperature
694:mL / 100 mL
607:cardinality
594:ISO 80000-1
495:independent
472:Boyle's Law
308:proved the
213:derivatives
167:milliliters
2349:(15 pages)
2255:2022-06-13
2230:2015-10-07
2169:2015-10-07
2109:Metrologia
2092:2023-11-03
2063:2023-07-23
2036:2021-11-30
1995:2021-11-30
1886:2010-01-22
1855:2010-01-22
1761:2022-12-21
1410:Metrologia
1386:Metrologia
1342:2011-03-22
1306:References
1290:statistics
1248:Elasticity
1242:efficiency
814:, and the
737:dispersion
721:statistics
630:Count data
514:quantities
498:dimensions
479:functional
440:April 2022
266:See also:
241:relativity
235:, and the
197:parameters
174:number one
112:March 2017
82:newspapers
2325:0263-2241
2317:1873-412X
2146:122242959
2138:0026-1394
1809:1476-4687
1732:1476-4687
1619:0743-7463
1524:1008.3907
1438:0026-1394
1201:Chemistry
1166:≫
1161:∗
1128:∗
1100:≈
1095:∗
1068:∗
936:ℏ
893:rest mass
717:steradian
561:Dimension
487:variables
411:does not
290:dimension
245:chemistry
2376:Category
2343:33311828
1972:(2017).
1917:15588029
1903:(2004).
1825:52806576
1817:28905893
1766:(1 page)
1752:Archived
1740:28796224
1643:(1914).
1627:27504666
1599:Langmuir
1549:22181590
1261:See also
901:electron
656:or some
588:(symbol
554:Unitless
524:Integers
518:quantity
468:identity
205:calculus
2334:7727271
2297:Bibcode
2118:Bibcode
2058:iso.org
1944:Bibcode
1748:4444368
1712:Bibcode
1659:Bibcode
1529:Bibcode
1418:Bibcode
1240:is the
895:of the
739:in the
731:to the
686:ethanol
676:/kg or
432:removed
417:sources
338:decibel
313:theorem
262:History
182:Radians
96:scholar
2341:
2331:
2323:
2315:
2144:
2136:
2027:
1986:
1915:
1823:
1815:
1807:
1786:Nature
1746:
1738:
1730:
1703:Nature
1625:
1617:
1547:
1488:
1461:
1436:
1338:. 2008
1324:(1.6)
1052:pipes.
897:proton
834:, and
832:charge
824:length
810:, the
806:, the
774:× dim
770:= dim
715:, and
713:radian
688:in an
654:slopes
650:ratios
361:torque
353:radian
349:Nature
333:levels
227:, the
209:limits
190:radius
147:ratios
98:
91:
84:
77:
69:
2313:eISSN
2249:(PDF)
2142:S2CID
2081:(PDF)
1880:(PDF)
1873:(PDF)
1849:(PDF)
1842:(PDF)
1821:S2CID
1755:(PDF)
1744:S2CID
1698:(PDF)
1519:arXiv
1211:water
592:) in
493:) of
485:) of
345:op-ed
243:. In
151:units
103:JSTOR
89:books
2339:PMID
2321:ISSN
2134:ISSN
2025:ISBN
1984:ISBN
1913:PMID
1813:PMID
1805:ISSN
1736:PMID
1728:ISSN
1623:PMID
1615:ISSN
1545:PMID
1486:ISBN
1459:ISBN
1434:ISSN
1361:BIPM
1284:and
1133:<
966:List
920:≈ 1;
883:(or
828:mass
820:time
766:dim
741:data
733:mean
723:the
709:turn
618:bits
600:and
415:any
413:cite
326:and
300:and
294:unit
292:and
172:The
75:news
2329:PMC
2305:doi
2289:109
2197:doi
2126:doi
1952:doi
1795:doi
1791:549
1720:doi
1708:548
1675:hdl
1667:doi
1607:doi
1576:doi
1537:doi
1515:107
1426:doi
1336:ISO
1322:1.8
678:mol
664:or
426:by
377:uno
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347:in
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1950:.
1938:.
1934:.
1907:.
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918:s
915:α
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885:μ
881:β
871:α
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506:n
502:p
491:k
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Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
