74:
962:
146:
Moody's team used the available data (including that of
Nikuradse) to show that fluid flow in rough pipes could be described by four dimensionless quantities: Reynolds number, pressure loss coefficient, diameter ratio of the pipe and the relative roughness of the pipe. They then produced a single
137:
The chart's purpose was to provide a graphical representation of the function of C. F. Colebrook in collaboration with C. M. White, which provided a practical form of transition curve to bridge the transition zone between smooth and rough pipes, the region of incomplete turbulence.
832:
432:
1098:
735:
305:
355:
793:
607:
957:{\displaystyle {1 \over {\sqrt {f_{D}}}}=-2.0\log _{10}\left({\frac {\epsilon /D}{3.7}}+{\frac {2.51}{\mathrm {Re} {\sqrt {f_{D}}}}}\right),{\text{for turbulent flow}}.}
168:
1026:
824:
765:
671:
575:
502:
455:
226:
195:
641:
998:
542:
522:
475:
147:
plot which showed that all of these collapsed onto a series of lines, now known as the Moody chart. This dimensionless chart is used to work out pressure drop,
130:, whose work was based upon an analysis of some 10,000 experiments from various sources. Measurements of fluid flow in artificially roughened pipes by
1150:
366:
1034:
683:
234:
1132:
1270:
581:
Re for a variety of relative roughnesses, the ratio of the mean height of roughness of the pipe to the pipe diameter or
198:
103:
47:
1234:"Turbulent Flow in Pipes, With Particular Reference to the Transition Region Between the Smooth and Rough Pipe Laws"
316:
1205:
1285:
977:
644:
548:
43:
973:
1290:
796:
770:
584:
150:
111:
99:
63:
1245:
1233:
131:
1004:
802:
743:
649:
553:
480:
440:
204:
173:
70:
in a circular pipe. It can be used to predict pressure drop or flow rate down such a pipe.
1295:
578:
127:
107:
59:
623:
1218:
These show in detail the transition region for pipes with high relative roughness (ε /
983:
617:
527:
507:
460:
1279:
1265:
1117:
613:
123:
86:
plotted against
Reynolds number Re for various relative roughness ε /
674:
1249:
17:
740:
For the turbulent flow regime, the relationship between the friction factor
67:
1155:. Proceedings Second Hydraulic Conference, University of Iowa Bulletin 27.
643:< ~3000), roughness has no discernible effect, and the Darcy–Weisbach
1185:
Kemler, E. (1933). "A Study of the Data on the Flow of Fluid in Pipes".
197:(m)) and flow rate through pipes. Head loss can be calculated using the
427:{\displaystyle \Delta p=f_{D}{\frac {\rho V^{2}}{2}}{\frac {L}{D}},}
73:
1166:
Pigott, R. J. S. (1933). "The Flow of Fluids in Closed
Conduits".
1093:{\displaystyle \Delta p={\frac {\rho V^{2}}{2}}{\frac {4fL}{D}},}
730:{\displaystyle f_{D}=64/\mathrm {Re} ,{\text{for laminar flow}}.}
300:{\displaystyle h_{f}=f_{D}{\frac {L}{D}}{\frac {V^{2}}{2\,g}};}
126:
but uses the more practical choice of coordinates employed by
134:
were at the time too recent to include in Pigott's chart.
1001:, equal to one fourth the Darcy-Weisbach friction factor
612:
The Moody chart can be divided into two regimes of flow:
77:
Moody diagram showing the Darcy–Weisbach friction factor
795:
is more complex. One model for this relationship is the
1037:
1007:
986:
835:
805:
773:
746:
686:
652:
626:
587:
556:
530:
510:
483:
463:
443:
369:
319:
237:
207:
176:
153:
767:
the
Reynolds number Re, and the relative roughness
1092:
1020:
992:
956:
818:
787:
759:
729:
665:
635:
601:
569:
536:
516:
496:
469:
449:
426:
349:
299:
220:
189:
162:
1238:Journal of the Institution of Civil Engineers
504:is the friction factor from the Moody chart,
8:
972:This formula must not be confused with the
118:. This chart became commonly known as the
1069:
1057:
1047:
1036:
1012:
1006:
985:
946:
927:
921:
913:
907:
890:
884:
870:
847:
841:
836:
834:
810:
804:
777:
772:
751:
745:
719:
708:
703:
691:
685:
657:
651:
625:
591:
586:
561:
555:
529:
509:
488:
482:
462:
442:
411:
399:
389:
383:
368:
341:
336:
332:
318:
287:
277:
271:
261:
255:
242:
236:
212:
206:
181:
175:
152:
122:or Moody diagram. It adapts the work of
350:{\displaystyle \Delta p=\rho \,g\,h_{f}}
310:Pressure drop can then be evaluated as:
72:
1108:
477:is the average velocity in the pipe,
7:
201:in which the Darcy friction factor
1206:"Strömungsgesetze in Rauen Rohren"
1038:
917:
914:
799:(which is an implicit equation in
712:
709:
370:
320:
154:
110:Re for various values of relative
25:
1152:Evaluation of Boundary Roughness
1118:"Friction factors for pipe flow"
1244:(4). London, England: 133–156.
1138:from the original on 2019-11-26
673:was determined analytically by
620:. For the laminar flow regime (
547:The chart plots Darcy–Weisbach
1271:Darcy friction factor formulae
1232:Colebrook, C. F. (1938–1939).
524:is the length of the pipe and
104:Darcy–Weisbach friction factor
48:Darcy–Weisbach friction factor
1:
1028:. Here the pressure drop is:
457:is the density of the fluid,
27:Graph used in fluid dynamics
788:{\displaystyle \epsilon /D}
602:{\displaystyle \epsilon /D}
1312:
1250:10.1680/ijoti.1939.13150
1187:Transactions of the ASME
1125:Transactions of the ASME
163:{\displaystyle \Delta p}
1210:V. D. I. Forschungsheft
978:Fanning friction factor
968:Fanning friction factor
199:Darcy–Weisbach equation
1204:Nikuradse, J. (1933).
1168:Mechanical Engineering
1094:
1022:
994:
958:
820:
789:
761:
731:
667:
637:
603:
571:
544:is the pipe diameter.
538:
518:
498:
471:
451:
428:
351:
301:
222:
191:
164:
90:
46:form that relates the
1116:Moody, L. F. (1944),
1095:
1023:
1021:{\displaystyle f_{D}}
995:
959:
821:
819:{\displaystyle f_{D}}
790:
762:
760:{\displaystyle f_{D}}
732:
668:
666:{\displaystyle f_{D}}
638:
604:
572:
570:{\displaystyle f_{D}}
539:
519:
499:
497:{\displaystyle f_{D}}
472:
452:
450:{\displaystyle \rho }
429:
352:
302:
223:
221:{\displaystyle f_{D}}
192:
190:{\displaystyle h_{f}}
165:
76:
1035:
1005:
984:
833:
803:
771:
744:
684:
650:
624:
585:
554:
528:
508:
481:
461:
441:
367:
317:
235:
205:
174:
170:(Pa) (or head loss,
151:
66:for fully developed
30:In engineering, the
1149:Rouse, H. (1943).
1090:
1018:
990:
954:
948:for turbulent flow
816:
797:Colebrook equation
785:
757:
727:
663:
636:{\displaystyle Re}
633:
599:
567:
534:
514:
494:
467:
447:
424:
347:
297:
218:
187:
160:
91:
1193:(Hyd-55-2): 7–32.
1085:
1067:
993:{\displaystyle f}
949:
936:
933:
902:
855:
853:
722:
537:{\displaystyle D}
517:{\displaystyle L}
470:{\displaystyle V}
419:
409:
360:or directly from
292:
269:
100:Lewis Ferry Moody
64:surface roughness
16:(Redirected from
1303:
1254:
1253:
1229:
1223:
1217:
1201:
1195:
1194:
1182:
1176:
1175:
1163:
1157:
1156:
1146:
1140:
1139:
1137:
1122:
1113:
1099:
1097:
1096:
1091:
1086:
1081:
1070:
1068:
1063:
1062:
1061:
1048:
1027:
1025:
1024:
1019:
1017:
1016:
999:
997:
996:
991:
974:Fanning equation
963:
961:
960:
955:
950:
947:
942:
938:
937:
935:
934:
932:
931:
922:
920:
908:
903:
898:
894:
885:
875:
874:
856:
854:
852:
851:
842:
837:
825:
823:
822:
817:
815:
814:
794:
792:
791:
786:
781:
766:
764:
763:
758:
756:
755:
736:
734:
733:
728:
723:
721:for laminar flow
720:
715:
707:
696:
695:
672:
670:
669:
664:
662:
661:
642:
640:
639:
634:
608:
606:
605:
600:
595:
576:
574:
573:
568:
566:
565:
543:
541:
540:
535:
523:
521:
520:
515:
503:
501:
500:
495:
493:
492:
476:
474:
473:
468:
456:
454:
453:
448:
433:
431:
430:
425:
420:
412:
410:
405:
404:
403:
390:
388:
387:
356:
354:
353:
348:
346:
345:
306:
304:
303:
298:
293:
291:
282:
281:
272:
270:
262:
260:
259:
247:
246:
227:
225:
224:
219:
217:
216:
196:
194:
193:
188:
186:
185:
169:
167:
166:
161:
42:) is a graph in
21:
1311:
1310:
1306:
1305:
1304:
1302:
1301:
1300:
1276:
1275:
1262:
1257:
1231:
1230:
1226:
1216:. Berlin: 1–22.
1203:
1202:
1198:
1184:
1183:
1179:
1174:: 497–501, 515.
1165:
1164:
1160:
1148:
1147:
1143:
1135:
1120:
1115:
1114:
1110:
1106:
1071:
1053:
1049:
1033:
1032:
1008:
1003:
1002:
982:
981:
970:
923:
912:
886:
883:
879:
866:
843:
831:
830:
806:
801:
800:
769:
768:
747:
742:
741:
687:
682:
681:
653:
648:
647:
645:friction factor
622:
621:
583:
582:
579:Reynolds number
557:
552:
551:
549:friction factor
526:
525:
506:
505:
484:
479:
478:
459:
458:
439:
438:
395:
391:
379:
365:
364:
337:
315:
314:
283:
273:
251:
238:
233:
232:
228:appears :
208:
203:
202:
177:
172:
171:
149:
148:
144:
128:R. J. S. Pigott
108:Reynolds number
96:
85:
60:Reynolds number
57:
44:non-dimensional
40:Stanton diagram
28:
23:
22:
15:
12:
11:
5:
1309:
1307:
1299:
1298:
1293:
1288:
1286:Fluid dynamics
1278:
1277:
1274:
1273:
1268:
1261:
1258:
1256:
1255:
1224:
1196:
1177:
1158:
1141:
1131:(8): 671–684,
1107:
1105:
1102:
1101:
1100:
1089:
1084:
1080:
1077:
1074:
1066:
1060:
1056:
1052:
1046:
1043:
1040:
1015:
1011:
989:
969:
966:
965:
964:
953:
945:
941:
930:
926:
919:
916:
911:
906:
901:
897:
893:
889:
882:
878:
873:
869:
865:
862:
859:
850:
846:
840:
813:
809:
784:
780:
776:
754:
750:
738:
737:
726:
718:
714:
711:
706:
702:
699:
694:
690:
660:
656:
632:
629:
598:
594:
590:
564:
560:
533:
513:
491:
487:
466:
446:
435:
434:
423:
418:
415:
408:
402:
398:
394:
386:
382:
378:
375:
372:
358:
357:
344:
340:
335:
331:
328:
325:
322:
308:
307:
296:
290:
286:
280:
276:
268:
265:
258:
254:
250:
245:
241:
215:
211:
184:
180:
159:
156:
143:
140:
95:
92:
81:
53:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
1308:
1297:
1294:
1292:
1289:
1287:
1284:
1283:
1281:
1272:
1269:
1267:
1266:Friction loss
1264:
1263:
1259:
1251:
1247:
1243:
1239:
1235:
1228:
1225:
1221:
1215:
1211:
1207:
1200:
1197:
1192:
1188:
1181:
1178:
1173:
1169:
1162:
1159:
1154:
1153:
1145:
1142:
1134:
1130:
1126:
1119:
1112:
1109:
1103:
1087:
1082:
1078:
1075:
1072:
1064:
1058:
1054:
1050:
1044:
1041:
1031:
1030:
1029:
1013:
1009:
1000:
987:
979:
975:
967:
951:
943:
939:
928:
924:
909:
904:
899:
895:
891:
887:
880:
876:
871:
867:
863:
860:
857:
848:
844:
838:
829:
828:
827:
811:
807:
798:
782:
778:
774:
752:
748:
724:
716:
704:
700:
697:
692:
688:
680:
679:
678:
676:
658:
654:
646:
630:
627:
619:
615:
610:
596:
592:
588:
580:
562:
558:
550:
545:
531:
511:
489:
485:
464:
444:
421:
416:
413:
406:
400:
396:
392:
384:
380:
376:
373:
363:
362:
361:
342:
338:
333:
329:
326:
323:
313:
312:
311:
294:
288:
284:
278:
274:
266:
263:
256:
252:
248:
243:
239:
231:
230:
229:
213:
209:
200:
182:
178:
157:
141:
139:
135:
133:
129:
125:
121:
117:
113:
109:
105:
101:
93:
89:
84:
80:
75:
71:
69:
65:
61:
56:
52:
49:
45:
41:
37:
36:Moody diagram
33:
19:
18:Moody diagram
1241:
1237:
1227:
1222:> 0.001).
1219:
1213:
1209:
1199:
1190:
1186:
1180:
1171:
1167:
1161:
1151:
1144:
1128:
1124:
1111:
980:
976:, using the
971:
739:
611:
546:
436:
359:
309:
145:
136:
132:J. Nikuradse
124:Hunter Rouse
119:
115:
102:plotted the
97:
87:
82:
78:
54:
50:
39:
35:
31:
29:
142:Description
120:Moody chart
32:Moody chart
1291:Hydraulics
1280:Categories
1104:References
675:Poiseuille
1051:ρ
1039:Δ
888:ϵ
877:
861:−
775:ϵ
618:turbulent
589:ϵ
445:ρ
393:ρ
371:Δ
330:ρ
321:Δ
155:Δ
112:roughness
98:In 1944,
1260:See also
1133:archived
577:against
106:against
62:Re, and
614:laminar
94:History
1296:Piping
437:where
38:(also
1136:(PDF)
1121:(PDF)
910:2.51
616:and
114:ε /
68:flow
1246:doi
1214:361
900:3.7
868:log
864:2.0
826:):
34:or
1282::
1242:11
1240:.
1236:.
1212:.
1208:.
1191:55
1189:.
1172:55
1170:.
1129:66
1127:,
1123:,
872:10
701:64
677::
609:.
58:,
1252:.
1248::
1220:D
1088:,
1083:D
1079:L
1076:f
1073:4
1065:2
1059:2
1055:V
1045:=
1042:p
1014:D
1010:f
988:f
952:.
944:,
940:)
929:D
925:f
918:e
915:R
905:+
896:D
892:/
881:(
858:=
849:D
845:f
839:1
812:D
808:f
783:D
779:/
753:D
749:f
725:.
717:,
713:e
710:R
705:/
698:=
693:D
689:f
659:D
655:f
631:e
628:R
597:D
593:/
563:D
559:f
532:D
512:L
490:D
486:f
465:V
422:,
417:D
414:L
407:2
401:2
397:V
385:D
381:f
377:=
374:p
343:f
339:h
334:g
327:=
324:p
295:;
289:g
285:2
279:2
275:V
267:D
264:L
257:D
253:f
249:=
244:f
240:h
214:D
210:f
183:f
179:h
158:p
116:D
88:D
83:D
79:f
55:D
51:f
20:)
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