353:
86:
998:
1277:
602:
1684:
313:
866:
1176:
504:
1400:
1113:
1531:
698:
226:
925:
976:
456:
1051:
175:
1596:
760:
404:
125:
1563:
1210:
545:
1426:
727:
256:
1474:
1454:
1344:
1324:
1304:
655:
632:
75:
340:
1218:
553:
1985:
1628:
264:
1977:
940:
classification, the equivalent diameter is the "diameter of a circle with an equal aggregate sectional area", which is calculated by
799:
1124:
467:
1349:
870:
as one would expect. This is equivalent to the above definition of the 2D mean diameter. However, for historical reasons, the
49:) is the radius of a circle or sphere with the same perimeter, area, or volume of a non-circular or non-spherical object. The
1903:
1067:
89:
Measurement of tree circumference, the tape calibrated to show diameter, at breast height. The tape assumes a circular shape.
339:, measured at height of 4.5 feet, divided by pi. This corresponds to the 1D mean diameter. It can be measured directly by a
1479:
660:
186:
1835:
1810:
885:
943:
420:
1016:
992:
17:
141:
1851:
Wei, Maoxing; Cheng, Nian-Sheng; Lu, Yesheng (October 2023). "Revisiting the concept of hydraulic radius".
1928:
1921:"Distorted, nonspherical transiting planets: impact on the transit depth and on the radius determination"
1746:
1568:
732:
1741:
332:
510:
1766:
988:
31:
1920:
937:
379:
364:
is the equivalent circular configuration with the same circumference as the wetted perimeter.
94:
1951:
104:
1994:
1947:
1860:
1536:
1433:
1188:
774:
523:
8:
1405:
1283:
706:
1998:
1864:
238:
1937:
1895:
1459:
1439:
1329:
1309:
1289:
1006:
770:
640:
617:
361:
60:
2006:
1899:
1831:
1806:
1725:
1717:
1713:
2002:
1955:
1891:
1868:
871:
782:
369:
357:
1959:
1872:
1756:
1697:
1429:
635:
612:
38:
27:
Radius of a circle or sphere equivalent to a non-circular or non-spherical object
2031:
2026:
1776:
2020:
326:
329:, rounded to the nearest 1/8 inch. This corresponds to the 1D mean diameter.
1781:
1761:
1729:
1706:
1702:
1001:
A sphere (top), rotational ellipsoid (left) and triaxial ellipsoid (right)
1272:{\displaystyle R_{\text{mean}}={\sqrt{\frac {3}{4\pi }}}L\approx 0.6204L}
597:{\displaystyle R_{\text{mean}}={\sqrt {\frac {1}{\pi }}}L\approx 0.3183L}
322:
1751:
356:
Cross sectional area of a trapezoidal open channel, red highlights the
336:
1721:
1679:{\displaystyle R={\sqrt{6378.1^{2}\cdot 6356.8}}=6371.0{\text{ km}}}
258:. Setting that perimeter to be equal to that of a circle imply that
1402:. The formula for a rotational ellipsoid is the special case where
352:
1942:
608:
325:
is the circumference of the head, measured in inches, divided by
308:{\displaystyle R_{\text{mean}}={\frac {2L}{\pi }}\approx 0.6366L}
85:
1212:. Setting that volume to be equal that of a sphere imply that
30:"Mean radius" redirects here. For the usage in astronomy, see
1771:
1609:, which can be approximated as an oblate spheroid with radii
1606:
997:
861:{\displaystyle D_{\text{H}}={\frac {4\pi R^{2}}{2\pi R}}=2R}
547:. Setting that area to be equal that of a circle imply that
1978:"Mean radius, mass, and inertia for reference Earth models"
1805:(5th ed.). Lexington, Mass: D.C. Heath. p. 512.
1171:{\displaystyle R_{\text{mean}}={\sqrt{\frac {3V}{4\pi }}}}
499:{\displaystyle R_{\text{mean}}={\sqrt {\frac {A}{\pi }}}}
1395:{\displaystyle R_{\text{mean}}={\sqrt{a\cdot b\cdot c}}}
1108:{\displaystyle V={\frac {4}{3}}\pi R_{\text{mean}}^{3}}
978:. It is used in many digital image processing programs.
1631:
1571:
1539:
1526:{\displaystyle R_{\text{mean}}={\sqrt{a^{2}\cdot c}}}
1482:
1462:
1442:
1408:
1352:
1332:
1312:
1292:
1221:
1191:
1127:
1070:
1019:
946:
888:
802:
735:
709:
663:
643:
620:
556:
526:
470:
423:
382:
267:
241:
189:
144:
107:
63:
1918:
1678:
1590:
1557:
1525:
1468:
1448:
1420:
1394:
1338:
1318:
1298:
1271:
1204:
1170:
1107:
1045:
970:
919:
860:
754:
721:
693:{\displaystyle R_{\text{mean}}={\sqrt {a\cdot b}}}
692:
649:
626:
596:
539:
498:
450:
398:
360:, where water is in contact with the channel. The
307:
250:
221:{\displaystyle R_{\text{mean}}={\frac {P}{2\pi }}}
220:
169:
119:
69:
874:is defined as the cross-sectional area of a pipe
2018:
127:. Given the perimeter of a non-circular object
1975:
1886:Sun, Lijun (2016). "Asphalt mix homogeneity".
1053:. Given the volume of an non-spherical object
920:{\displaystyle D_{\text{H}}=4R_{\mathbb {H} }}
1986:Physics of the Earth and Planetary Interiors
1800:
971:{\displaystyle D=2{\sqrt {\frac {A}{\pi }}}}
1919:Leconte, J.; Lai, D.; Chabrier, G. (2011).
1801:Bello, Ignacio; Britton, Jack Rolf (1993).
406:. Given the area of an non-circular object
1850:
1971:
1969:
1941:
911:
451:{\displaystyle A=\pi R_{\text{mean}}^{2}}
1888:Structural Behavior of Asphalt Pavements
996:
351:
84:
1046:{\displaystyle {\frac {4}{3}}\pi R^{3}}
509:Often the area considered is that of a
80:
14:
2019:
1966:
1912:
170:{\displaystyle P=2\pi R_{\text{mean}}}
1830:. New York: Springer. pp. 13ff.
1826:West, P. W. (2004). "Stem diameter".
1690:
516:For example, a square of side length
1825:
982:
773:is similarly defined as 4 times the
1885:
1181:For example, a cube of side length
24:
1896:10.1016/B978-0-12-849908-5.00013-4
1803:Topics in Contemporary Mathematics
1724:-equivalent radii at a particular
878:, divided by its wetted perimeter
347:
77:) is twice the equivalent radius.
25:
2043:
1976:Chambat, F.; Valette, B. (2001).
1732:and solid figures, respectively.
1591:{\displaystyle R_{\text{mean}}=a}
755:{\displaystyle R_{\text{mean}}=a}
788:. For a circular pipe of radius
1879:
1844:
1819:
1794:
927:, and the hydraulic radius is
231:For example, a square of side
13:
1:
2007:10.1016/S0031-9201(01)00200-X
1873:10.1016/j.jhydrol.2023.130134
1787:
993:Equivalent spherical diameter
1929:Astronomy & Astrophysics
7:
1960:10.1051/0004-6361/201015811
1828:Tree and Forest Measurement
1747:Cloud drop effective radius
1735:
133:perimeter-equivalent radius
10:
2048:
986:
29:
1742:Antenna equivalent radius
399:{\displaystyle \pi R^{2}}
333:Diameter at breast height
1625:, the 3D mean radius is
1059:volume-equivalent radius
1057:, one can calculate its
410:, one can calculate its
335:is the circumference of
131:, one can calculate its
1952:2011A&A...528A..41L
1767:Galaxy effective radius
1705:-equivalent radius for
989:Mean radius (astronomy)
792:, at full flow, this is
32:mean radius (astronomy)
1709:such as an ellipsoid.
1680:
1592:
1559:
1533:. For a sphere, where
1527:
1470:
1450:
1422:
1396:
1340:
1320:
1300:
1273:
1206:
1172:
1109:
1047:
1002:
972:
931:of the 2D mean radius.
921:
862:
756:
723:
694:
651:
628:
598:
541:
500:
452:
412:area-equivalent radius
400:
365:
309:
252:
222:
171:
121:
120:{\displaystyle 2\pi R}
90:
71:
1681:
1593:
1565:, this simplifies to
1560:
1558:{\displaystyle a=b=c}
1528:
1476:has a mean radius of
1471:
1451:
1423:
1397:
1341:
1321:
1301:
1274:
1207:
1205:{\displaystyle L^{3}}
1173:
1110:
1048:
1000:
987:Further information:
973:
922:
863:
757:
729:, this simplifies to
724:
695:
652:
629:
599:
542:
540:{\displaystyle L^{2}}
501:
453:
401:
355:
310:
253:
223:
172:
122:
95:perimeter of a circle
88:
72:
1890:. pp. 821–921.
1853:Journal of Hydrology
1629:
1569:
1537:
1480:
1460:
1440:
1434:rotational ellipsoid
1406:
1350:
1330:
1310:
1290:
1219:
1189:
1125:
1068:
1017:
944:
886:
800:
775:cross-sectional area
733:
707:
703:For a circle, where
661:
641:
618:
554:
524:
468:
421:
380:
265:
239:
187:
142:
105:
81:Perimeter equivalent
61:
1999:2001PEPI..124..237C
1865:2023JHyd..62530134W
1421:{\displaystyle a=b}
1284:tri-axial ellipsoid
1118:or, alternatively:
1104:
722:{\displaystyle a=b}
461:or, alternatively:
447:
235:has a perimeter of
180:or, alternatively:
51:equivalent diameter
1859:(Part B): 130134.
1691:Other equivalences
1676:
1588:
1555:
1523:
1466:
1446:
1418:
1392:
1336:
1316:
1296:
1269:
1202:
1168:
1105:
1090:
1043:
1007:volume of a sphere
1003:
968:
917:
858:
783:"wetted" perimeter
771:hydraulic diameter
752:
719:
690:
647:
624:
594:
537:
496:
448:
433:
396:
366:
362:hydraulic diameter
305:
251:{\displaystyle 4L}
248:
218:
167:
117:
91:
67:
1905:978-0-12-849908-5
1726:point of tangency
1718:osculating sphere
1714:osculating circle
1674:
1663:
1579:
1521:
1490:
1469:{\displaystyle c}
1449:{\displaystyle a}
1390:
1360:
1339:{\displaystyle c}
1319:{\displaystyle b}
1299:{\displaystyle a}
1255:
1249:
1229:
1166:
1160:
1135:
1097:
1085:
1028:
983:Volume equivalent
966:
965:
896:
882:, which leads to
847:
810:
781:, divided by its
743:
688:
671:
650:{\displaystyle b}
627:{\displaystyle a}
580:
579:
564:
494:
493:
478:
440:
294:
275:
216:
197:
164:
70:{\displaystyle D}
43:equivalent radius
16:(Redirected from
2039:
2011:
2010:
1982:
1973:
1964:
1963:
1945:
1925:
1916:
1910:
1909:
1883:
1877:
1876:
1848:
1842:
1841:
1823:
1817:
1816:
1798:
1685:
1683:
1682:
1677:
1675:
1672:
1664:
1662:
1657:
1650:
1649:
1639:
1624:
1622:
1616:
1614:
1597:
1595:
1594:
1589:
1581:
1580:
1577:
1564:
1562:
1561:
1556:
1532:
1530:
1529:
1524:
1522:
1520:
1515:
1508:
1507:
1497:
1492:
1491:
1488:
1475:
1473:
1472:
1467:
1455:
1453:
1452:
1447:
1427:
1425:
1424:
1419:
1401:
1399:
1398:
1393:
1391:
1389:
1384:
1367:
1362:
1361:
1358:
1346:has mean radius
1345:
1343:
1342:
1337:
1325:
1323:
1322:
1317:
1305:
1303:
1302:
1297:
1278:
1276:
1275:
1270:
1256:
1254:
1248:
1237:
1236:
1231:
1230:
1227:
1211:
1209:
1208:
1203:
1201:
1200:
1185:has a volume of
1177:
1175:
1174:
1169:
1167:
1165:
1159:
1151:
1143:
1142:
1137:
1136:
1133:
1114:
1112:
1111:
1106:
1103:
1098:
1095:
1086:
1078:
1052:
1050:
1049:
1044:
1042:
1041:
1029:
1021:
977:
975:
974:
969:
967:
958:
957:
926:
924:
923:
918:
916:
915:
914:
898:
897:
894:
872:hydraulic radius
867:
865:
864:
859:
848:
846:
835:
834:
833:
817:
812:
811:
808:
761:
759:
758:
753:
745:
744:
741:
728:
726:
725:
720:
699:
697:
696:
691:
689:
678:
673:
672:
669:
657:has mean radius
656:
654:
653:
648:
633:
631:
630:
625:
603:
601:
600:
595:
581:
572:
571:
566:
565:
562:
546:
544:
543:
538:
536:
535:
505:
503:
502:
497:
495:
486:
485:
480:
479:
476:
457:
455:
454:
449:
446:
441:
438:
405:
403:
402:
397:
395:
394:
370:area of a circle
358:wetted perimeter
314:
312:
311:
306:
295:
290:
282:
277:
276:
273:
257:
255:
254:
249:
227:
225:
224:
219:
217:
215:
204:
199:
198:
195:
176:
174:
173:
168:
166:
165:
162:
126:
124:
123:
118:
76:
74:
73:
68:
39:applied sciences
21:
2047:
2046:
2042:
2041:
2040:
2038:
2037:
2036:
2017:
2016:
2015:
2014:
1980:
1974:
1967:
1923:
1917:
1913:
1906:
1884:
1880:
1849:
1845:
1838:
1824:
1820:
1813:
1799:
1795:
1790:
1757:Earth ellipsoid
1738:
1698:authalic radius
1693:
1671:
1658:
1645:
1641:
1640:
1638:
1630:
1627:
1626:
1620:
1618:
1612:
1610:
1576:
1572:
1570:
1567:
1566:
1538:
1535:
1534:
1516:
1503:
1499:
1498:
1496:
1487:
1483:
1481:
1478:
1477:
1461:
1458:
1457:
1441:
1438:
1437:
1430:oblate spheroid
1428:. Likewise, an
1407:
1404:
1403:
1385:
1368:
1366:
1357:
1353:
1351:
1348:
1347:
1331:
1328:
1327:
1311:
1308:
1307:
1291:
1288:
1287:
1250:
1241:
1235:
1226:
1222:
1220:
1217:
1216:
1196:
1192:
1190:
1187:
1186:
1161:
1152:
1144:
1141:
1132:
1128:
1126:
1123:
1122:
1099:
1094:
1077:
1069:
1066:
1065:
1037:
1033:
1020:
1018:
1015:
1014:
995:
985:
956:
945:
942:
941:
910:
909:
905:
893:
889:
887:
884:
883:
836:
829:
825:
818:
816:
807:
803:
801:
798:
797:
740:
736:
734:
731:
730:
708:
705:
704:
677:
668:
664:
662:
659:
658:
642:
639:
638:
636:semi-minor axis
619:
616:
615:
613:semi-major axis
570:
561:
557:
555:
552:
551:
531:
527:
525:
522:
521:
520:has an area of
484:
475:
471:
469:
466:
465:
442:
437:
422:
419:
418:
390:
386:
381:
378:
377:
350:
348:Area equivalent
283:
281:
272:
268:
266:
263:
262:
240:
237:
236:
208:
203:
194:
190:
188:
185:
184:
161:
157:
143:
140:
139:
106:
103:
102:
83:
62:
59:
58:
35:
28:
23:
22:
15:
12:
11:
5:
2045:
2035:
2034:
2029:
2013:
2012:
1965:
1911:
1904:
1878:
1843:
1836:
1818:
1811:
1792:
1791:
1789:
1786:
1785:
1784:
1779:
1777:Geometric mean
1774:
1769:
1764:
1759:
1754:
1749:
1744:
1737:
1734:
1692:
1689:
1688:
1687:
1670:
1667:
1661:
1656:
1653:
1648:
1644:
1637:
1634:
1601:Applications:
1587:
1584:
1575:
1554:
1551:
1548:
1545:
1542:
1519:
1514:
1511:
1506:
1502:
1495:
1486:
1465:
1445:
1417:
1414:
1411:
1388:
1383:
1380:
1377:
1374:
1371:
1365:
1356:
1335:
1315:
1295:
1280:
1279:
1268:
1265:
1262:
1259:
1253:
1247:
1244:
1240:
1234:
1225:
1199:
1195:
1179:
1178:
1164:
1158:
1155:
1150:
1147:
1140:
1131:
1116:
1115:
1102:
1093:
1089:
1084:
1081:
1076:
1073:
1040:
1036:
1032:
1027:
1024:
984:
981:
980:
979:
964:
961:
955:
952:
949:
933:
932:
913:
908:
904:
901:
892:
868:
857:
854:
851:
845:
842:
839:
832:
828:
824:
821:
815:
806:
794:
793:
765:Applications:
751:
748:
739:
718:
715:
712:
687:
684:
681:
676:
667:
646:
623:
607:Similarly, an
605:
604:
593:
590:
587:
584:
578:
575:
569:
560:
534:
530:
507:
506:
492:
489:
483:
474:
459:
458:
445:
436:
432:
429:
426:
393:
389:
385:
349:
346:
345:
344:
330:
318:Applications:
316:
315:
304:
301:
298:
293:
289:
286:
280:
271:
247:
244:
229:
228:
214:
211:
207:
202:
193:
178:
177:
160:
156:
153:
150:
147:
116:
113:
110:
82:
79:
66:
26:
9:
6:
4:
3:
2:
2044:
2033:
2030:
2028:
2025:
2024:
2022:
2008:
2004:
2000:
1996:
1992:
1988:
1987:
1979:
1972:
1970:
1961:
1957:
1953:
1949:
1944:
1939:
1935:
1931:
1930:
1922:
1915:
1907:
1901:
1897:
1893:
1889:
1882:
1874:
1870:
1866:
1862:
1858:
1854:
1847:
1839:
1837:9783540403906
1833:
1829:
1822:
1814:
1812:9780669289572
1808:
1804:
1797:
1793:
1783:
1780:
1778:
1775:
1773:
1770:
1768:
1765:
1763:
1760:
1758:
1755:
1753:
1750:
1748:
1745:
1743:
1740:
1739:
1733:
1731:
1730:plane figures
1727:
1723:
1719:
1715:
1710:
1708:
1707:solid figures
1704:
1700:
1699:
1668:
1665:
1659:
1654:
1651:
1646:
1642:
1635:
1632:
1608:
1604:
1603:
1602:
1599:
1585:
1582:
1573:
1552:
1549:
1546:
1543:
1540:
1517:
1512:
1509:
1504:
1500:
1493:
1484:
1463:
1443:
1435:
1431:
1415:
1412:
1409:
1386:
1381:
1378:
1375:
1372:
1369:
1363:
1354:
1333:
1313:
1293:
1285:
1282:Similarly, a
1266:
1263:
1260:
1257:
1251:
1245:
1242:
1238:
1232:
1223:
1215:
1214:
1213:
1197:
1193:
1184:
1162:
1156:
1153:
1148:
1145:
1138:
1129:
1121:
1120:
1119:
1100:
1091:
1087:
1082:
1079:
1074:
1071:
1064:
1063:
1062:
1060:
1056:
1038:
1034:
1030:
1025:
1022:
1012:
1008:
999:
994:
990:
962:
959:
953:
950:
947:
939:
935:
934:
930:
906:
902:
899:
890:
881:
877:
873:
869:
855:
852:
849:
843:
840:
837:
830:
826:
822:
819:
813:
804:
796:
795:
791:
787:
784:
780:
776:
772:
768:
767:
766:
763:
749:
746:
737:
716:
713:
710:
701:
685:
682:
679:
674:
665:
644:
637:
621:
614:
610:
591:
588:
585:
582:
576:
573:
567:
558:
550:
549:
548:
532:
528:
519:
514:
512:
511:cross section
490:
487:
481:
472:
464:
463:
462:
443:
434:
430:
427:
424:
417:
416:
415:
413:
409:
391:
387:
383:
375:
371:
363:
359:
354:
342:
341:girthing tape
338:
334:
331:
328:
324:
321:
320:
319:
302:
299:
296:
291:
287:
284:
278:
269:
261:
260:
259:
245:
242:
234:
212:
209:
205:
200:
191:
183:
182:
181:
158:
154:
151:
148:
145:
138:
137:
136:
134:
130:
114:
111:
108:
100:
96:
87:
78:
64:
56:
55:mean diameter
52:
48:
44:
40:
33:
19:
18:Mean diameter
1990:
1984:
1933:
1927:
1914:
1887:
1881:
1856:
1852:
1846:
1827:
1821:
1802:
1796:
1782:Semidiameter
1762:Earth radius
1711:
1703:surface area
1696:
1694:
1600:
1281:
1182:
1180:
1117:
1058:
1054:
1010:
1004:
928:
879:
875:
789:
785:
778:
764:
702:
606:
517:
515:
508:
460:
411:
407:
373:
367:
317:
232:
230:
179:
132:
128:
98:
92:
54:
50:
46:
42:
36:
1605:For planet
1061:by setting
414:by setting
323:US hat size
135:by setting
47:mean radius
2021:Categories
1993:(3–4): 4.
1936:(A41): 9.
1788:References
1752:Cubic mean
1623:.8 km
1615:.1 km
1436:with axes
1286:with axes
1009:of radius
777:of a pipe
372:of radius
337:tree trunk
97:of radius
1943:1101.2813
1722:curvature
1652:⋅
1510:⋅
1379:⋅
1373:⋅
1261:≈
1246:π
1157:π
1088:π
1031:π
963:π
938:aggregate
841:π
823:π
683:⋅
586:≈
577:π
491:π
431:π
384:π
297:≈
292:π
213:π
155:π
112:π
1736:See also
1673: km
1995:Bibcode
1948:Bibcode
1861:Bibcode
1720:define
609:ellipse
1902:
1834:
1809:
1701:is an
1669:6371.0
1655:6356.8
1643:6378.1
1264:0.6204
589:0.3183
300:0.6366
41:, the
2032:Means
2027:Radii
1981:(PDF)
1938:arXiv
1924:(PDF)
1772:Geoid
1607:Earth
611:with
1900:ISBN
1832:ISBN
1807:ISBN
1728:for
1716:and
1712:The
1695:The
1617:and
1578:mean
1489:mean
1456:and
1359:mean
1326:and
1228:mean
1134:mean
1096:mean
1005:The
991:and
929:half
769:The
742:mean
670:mean
634:and
563:mean
477:mean
439:mean
368:The
274:mean
196:mean
163:mean
93:The
53:(or
45:(or
2003:doi
1991:124
1956:doi
1934:528
1892:doi
1869:doi
1857:625
1621:356
1613:378
1432:or
1013:is
936:In
376:is
101:is
57:) (
37:In
2023::
2001:.
1989:.
1983:.
1968:^
1954:.
1946:.
1932:.
1926:.
1898:.
1867:.
1855:.
1598:.
1306:,
762:.
700:.
513:.
327:pi
2009:.
2005::
1997::
1962:.
1958::
1950::
1940::
1908:.
1894::
1875:.
1871::
1863::
1840:.
1815:.
1686:.
1666:=
1660:3
1647:2
1636:=
1633:R
1619:6
1611:6
1586:a
1583:=
1574:R
1553:c
1550:=
1547:b
1544:=
1541:a
1518:3
1513:c
1505:2
1501:a
1494:=
1485:R
1464:c
1444:a
1416:b
1413:=
1410:a
1387:3
1382:c
1376:b
1370:a
1364:=
1355:R
1334:c
1314:b
1294:a
1267:L
1258:L
1252:3
1243:4
1239:3
1233:=
1224:R
1198:3
1194:L
1183:L
1163:3
1154:4
1149:V
1146:3
1139:=
1130:R
1101:3
1092:R
1083:3
1080:4
1075:=
1072:V
1055:V
1039:3
1035:R
1026:3
1023:4
1011:R
960:A
954:2
951:=
948:D
912:H
907:R
903:4
900:=
895:H
891:D
880:P
876:A
856:R
853:2
850:=
844:R
838:2
831:2
827:R
820:4
814:=
809:H
805:D
790:R
786:P
779:A
750:a
747:=
738:R
717:b
714:=
711:a
686:b
680:a
675:=
666:R
645:b
622:a
592:L
583:L
574:1
568:=
559:R
533:2
529:L
518:L
488:A
482:=
473:R
444:2
435:R
428:=
425:A
408:A
392:2
388:R
374:R
343:.
303:L
288:L
285:2
279:=
270:R
246:L
243:4
233:L
210:2
206:P
201:=
192:R
159:R
152:2
149:=
146:P
129:P
115:R
109:2
99:R
65:D
34:.
20:)
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