63:
951:
135:
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
126:
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.
821:
421:
1087:
724:
294:
344:
782:
596:
946:{\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}}.}
157:
1015:
813:
754:
660:
564:
491:
444:
215:
184:
630:
987:
531:
511:
464:
136:
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,
119:, whose work was based upon an analysis of some 10,000 experiments from various sources. Measurements of fluid flow in artificially roughened pipes by
1139:
355:
1023:
672:
223:
1121:
1259:
570:
Re for a variety of relative roughnesses, the ratio of the mean height of roughness of the pipe to the pipe diameter or
187:
92:
36:
1223:"Turbulent Flow in Pipes, With Particular Reference to the Transition Region Between the Smooth and Rough Pipe Laws"
305:
1194:
1274:
966:
633:
537:
32:
962:
1279:
785:
759:
573:
139:
100:
88:
52:
1234:
1222:
120:
993:
791:
732:
638:
542:
469:
429:
193:
162:
59:
in a circular pipe. It can be used to predict pressure drop or flow rate down such a pipe.
1284:
567:
116:
96:
48:
612:
1207:
These show in detail the transition region for pipes with high relative roughness (ε /
972:
606:
516:
496:
449:
1268:
1254:
1106:
602:
112:
75:
plotted against
Reynolds number Re for various relative roughness ε /
663:
1238:
729:
For the turbulent flow regime, the relationship between the friction factor
56:
1144:. Proceedings Second Hydraulic Conference, University of Iowa Bulletin 27.
632:< ~3000), roughness has no discernible effect, and the Darcy–Weisbach
1174:
Kemler, E. (1933). "A Study of the Data on the Flow of Fluid in Pipes".
186:(m)) and flow rate through pipes. Head loss can be calculated using the
416:{\displaystyle \Delta p=f_{D}{\frac {\rho V^{2}}{2}}{\frac {L}{D}},}
62:
1155:
Pigott, R. J. S. (1933). "The Flow of Fluids in Closed
Conduits".
1082:{\displaystyle \Delta p={\frac {\rho V^{2}}{2}}{\frac {4fL}{D}},}
719:{\displaystyle f_{D}=64/\mathrm {Re} ,{\text{for laminar flow}}.}
289:{\displaystyle h_{f}=f_{D}{\frac {L}{D}}{\frac {V^{2}}{2\,g}};}
115:
but uses the more practical choice of coordinates employed by
123:
were at the time too recent to include in Pigott's chart.
990:, equal to one fourth the Darcy-Weisbach friction factor
601:
The Moody chart can be divided into two regimes of flow:
66:
Moody diagram showing the Darcy–Weisbach friction factor
784:
is more complex. One model for this relationship is the
1026:
996:
975:
824:
794:
762:
735:
675:
641:
615:
576:
545:
519:
499:
472:
452:
432:
358:
308:
226:
196:
165:
142:
756:
the
Reynolds number Re, and the relative roughness
1081:
1009:
981:
945:
807:
776:
748:
718:
654:
624:
590:
558:
525:
505:
485:
458:
438:
415:
338:
288:
209:
178:
151:
1227:Journal of the Institution of Civil Engineers
493:is the friction factor from the Moody chart,
8:
961:This formula must not be confused with the
107:. This chart became commonly known as the
1058:
1046:
1036:
1025:
1001:
995:
974:
935:
916:
910:
902:
896:
879:
873:
859:
836:
830:
825:
823:
799:
793:
766:
761:
740:
734:
708:
697:
692:
680:
674:
646:
640:
614:
580:
575:
550:
544:
518:
498:
477:
471:
451:
431:
400:
388:
378:
372:
357:
330:
325:
321:
307:
276:
266:
260:
250:
244:
231:
225:
201:
195:
170:
164:
141:
111:or Moody diagram. It adapts the work of
339:{\displaystyle \Delta p=\rho \,g\,h_{f}}
299:Pressure drop can then be evaluated as:
61:
1097:
466:is the average velocity in the pipe,
7:
190:in which the Darcy friction factor
1195:"Strömungsgesetze in Rauen Rohren"
1027:
906:
903:
788:(which is an implicit equation in
701:
698:
359:
309:
143:
99:Re for various values of relative
14:
1141:Evaluation of Boundary Roughness
1107:"Friction factors for pipe flow"
1233:(4). London, England: 133–156.
1127:from the original on 2019-11-26
662:was determined analytically by
609:. For the laminar flow regime (
536:The chart plots Darcy–Weisbach
1260:Darcy friction factor formulae
1221:Colebrook, C. F. (1938–1939).
513:is the length of the pipe and
93:Darcy–Weisbach friction factor
37:Darcy–Weisbach friction factor
1:
1017:. Here the pressure drop is:
446:is the density of the fluid,
16:Graph used in fluid dynamics
777:{\displaystyle \epsilon /D}
591:{\displaystyle \epsilon /D}
1301:
1239:10.1680/ijoti.1939.13150
1176:Transactions of the ASME
1114:Transactions of the ASME
152:{\displaystyle \Delta p}
1199:V. D. I. Forschungsheft
967:Fanning friction factor
957:Fanning friction factor
188:Darcy–Weisbach equation
1193:Nikuradse, J. (1933).
1157:Mechanical Engineering
1083:
1011:
983:
947:
809:
778:
750:
720:
656:
626:
592:
560:
533:is the pipe diameter.
527:
507:
487:
460:
440:
417:
340:
290:
211:
180:
153:
79:
35:form that relates the
1105:Moody, L. F. (1944),
1084:
1012:
1010:{\displaystyle f_{D}}
984:
948:
810:
808:{\displaystyle f_{D}}
779:
751:
749:{\displaystyle f_{D}}
721:
657:
655:{\displaystyle f_{D}}
627:
593:
561:
559:{\displaystyle f_{D}}
528:
508:
488:
486:{\displaystyle f_{D}}
461:
441:
439:{\displaystyle \rho }
418:
341:
291:
212:
210:{\displaystyle f_{D}}
181:
179:{\displaystyle h_{f}}
154:
65:
1024:
994:
973:
822:
792:
760:
733:
673:
639:
613:
574:
543:
517:
497:
470:
450:
430:
356:
306:
224:
194:
163:
159:(Pa) (or head loss,
140:
55:for fully developed
19:In engineering, the
1138:Rouse, H. (1943).
1079:
1007:
979:
943:
937:for turbulent flow
805:
786:Colebrook equation
774:
746:
716:
652:
625:{\displaystyle Re}
622:
588:
556:
523:
503:
483:
456:
436:
413:
336:
286:
207:
176:
149:
80:
1182:(Hyd-55-2): 7–32.
1074:
1056:
982:{\displaystyle f}
938:
925:
922:
891:
844:
842:
711:
526:{\displaystyle D}
506:{\displaystyle L}
459:{\displaystyle V}
408:
398:
349:or directly from
281:
258:
89:Lewis Ferry Moody
53:surface roughness
1292:
1243:
1242:
1218:
1212:
1206:
1190:
1184:
1183:
1171:
1165:
1164:
1152:
1146:
1145:
1135:
1129:
1128:
1126:
1111:
1102:
1088:
1086:
1085:
1080:
1075:
1070:
1059:
1057:
1052:
1051:
1050:
1037:
1016:
1014:
1013:
1008:
1006:
1005:
988:
986:
985:
980:
963:Fanning equation
952:
950:
949:
944:
939:
936:
931:
927:
926:
924:
923:
921:
920:
911:
909:
897:
892:
887:
883:
874:
864:
863:
845:
843:
841:
840:
831:
826:
814:
812:
811:
806:
804:
803:
783:
781:
780:
775:
770:
755:
753:
752:
747:
745:
744:
725:
723:
722:
717:
712:
710:for laminar flow
709:
704:
696:
685:
684:
661:
659:
658:
653:
651:
650:
631:
629:
628:
623:
597:
595:
594:
589:
584:
565:
563:
562:
557:
555:
554:
532:
530:
529:
524:
512:
510:
509:
504:
492:
490:
489:
484:
482:
481:
465:
463:
462:
457:
445:
443:
442:
437:
422:
420:
419:
414:
409:
401:
399:
394:
393:
392:
379:
377:
376:
345:
343:
342:
337:
335:
334:
295:
293:
292:
287:
282:
280:
271:
270:
261:
259:
251:
249:
248:
236:
235:
216:
214:
213:
208:
206:
205:
185:
183:
182:
177:
175:
174:
158:
156:
155:
150:
31:) is a graph in
1300:
1299:
1295:
1294:
1293:
1291:
1290:
1289:
1265:
1264:
1251:
1246:
1220:
1219:
1215:
1205:. Berlin: 1–22.
1192:
1191:
1187:
1173:
1172:
1168:
1163:: 497–501, 515.
1154:
1153:
1149:
1137:
1136:
1132:
1124:
1109:
1104:
1103:
1099:
1095:
1060:
1042:
1038:
1022:
1021:
997:
992:
991:
971:
970:
959:
912:
901:
875:
872:
868:
855:
832:
820:
819:
795:
790:
789:
758:
757:
736:
731:
730:
676:
671:
670:
642:
637:
636:
634:friction factor
611:
610:
572:
571:
568:Reynolds number
546:
541:
540:
538:friction factor
515:
514:
495:
494:
473:
468:
467:
448:
447:
428:
427:
384:
380:
368:
354:
353:
326:
304:
303:
272:
262:
240:
227:
222:
221:
217:appears :
197:
192:
191:
166:
161:
160:
138:
137:
133:
117:R. J. S. Pigott
97:Reynolds number
85:
74:
49:Reynolds number
46:
33:non-dimensional
29:Stanton diagram
17:
12:
11:
5:
1298:
1296:
1288:
1287:
1282:
1277:
1275:Fluid dynamics
1267:
1266:
1263:
1262:
1257:
1250:
1247:
1245:
1244:
1213:
1185:
1166:
1147:
1130:
1120:(8): 671–684,
1096:
1094:
1091:
1090:
1089:
1078:
1073:
1069:
1066:
1063:
1055:
1049:
1045:
1041:
1035:
1032:
1029:
1004:
1000:
978:
958:
955:
954:
953:
942:
934:
930:
919:
915:
908:
905:
900:
895:
890:
886:
882:
878:
871:
867:
862:
858:
854:
851:
848:
839:
835:
829:
802:
798:
773:
769:
765:
743:
739:
727:
726:
715:
707:
703:
700:
695:
691:
688:
683:
679:
649:
645:
621:
618:
587:
583:
579:
553:
549:
522:
502:
480:
476:
455:
435:
424:
423:
412:
407:
404:
397:
391:
387:
383:
375:
371:
367:
364:
361:
347:
346:
333:
329:
324:
320:
317:
314:
311:
297:
296:
285:
279:
275:
269:
265:
257:
254:
247:
243:
239:
234:
230:
204:
200:
173:
169:
148:
145:
132:
129:
84:
81:
70:
42:
15:
13:
10:
9:
6:
4:
3:
2:
1297:
1286:
1283:
1281:
1278:
1276:
1273:
1272:
1270:
1261:
1258:
1256:
1255:Friction loss
1253:
1252:
1248:
1240:
1236:
1232:
1228:
1224:
1217:
1214:
1210:
1204:
1200:
1196:
1189:
1186:
1181:
1177:
1170:
1167:
1162:
1158:
1151:
1148:
1143:
1142:
1134:
1131:
1123:
1119:
1115:
1108:
1101:
1098:
1092:
1076:
1071:
1067:
1064:
1061:
1053:
1047:
1043:
1039:
1033:
1030:
1020:
1019:
1018:
1002:
998:
989:
976:
968:
964:
956:
940:
932:
928:
917:
913:
898:
893:
888:
884:
880:
876:
869:
865:
860:
856:
852:
849:
846:
837:
833:
827:
818:
817:
816:
800:
796:
787:
771:
767:
763:
741:
737:
713:
705:
693:
689:
686:
681:
677:
669:
668:
667:
665:
647:
643:
635:
619:
616:
608:
604:
599:
585:
581:
577:
569:
551:
547:
539:
534:
520:
500:
478:
474:
453:
433:
410:
405:
402:
395:
389:
385:
381:
373:
369:
365:
362:
352:
351:
350:
331:
327:
322:
318:
315:
312:
302:
301:
300:
283:
277:
273:
267:
263:
255:
252:
245:
241:
237:
232:
228:
220:
219:
218:
202:
198:
189:
171:
167:
146:
130:
128:
124:
122:
118:
114:
110:
106:
102:
98:
94:
90:
82:
78:
73:
69:
64:
60:
58:
54:
50:
45:
41:
38:
34:
30:
26:
25:Moody diagram
22:
1230:
1226:
1216:
1211:> 0.001).
1208:
1202:
1198:
1188:
1179:
1175:
1169:
1160:
1156:
1150:
1140:
1133:
1117:
1113:
1100:
969:
965:, using the
960:
728:
600:
535:
425:
348:
298:
134:
125:
121:J. Nikuradse
113:Hunter Rouse
108:
104:
91:plotted the
86:
76:
71:
67:
43:
39:
28:
24:
20:
18:
131:Description
109:Moody chart
21:Moody chart
1280:Hydraulics
1269:Categories
1093:References
664:Poiseuille
1040:ρ
1028:Δ
877:ϵ
866:
850:−
764:ϵ
607:turbulent
578:ϵ
434:ρ
382:ρ
360:Δ
319:ρ
310:Δ
144:Δ
101:roughness
87:In 1944,
1249:See also
1122:archived
566:against
95:against
51:Re, and
603:laminar
83:History
1285:Piping
426:where
27:(also
1125:(PDF)
1110:(PDF)
899:2.51
605:and
103:ε /
57:flow
1235:doi
1203:361
889:3.7
857:log
853:2.0
815:):
23:or
1271::
1231:11
1229:.
1225:.
1201:.
1197:.
1180:55
1178:.
1161:55
1159:.
1118:66
1116:,
1112:,
861:10
690:64
666::
598:.
47:,
1241:.
1237::
1209:D
1077:,
1072:D
1068:L
1065:f
1062:4
1054:2
1048:2
1044:V
1034:=
1031:p
1003:D
999:f
977:f
941:.
933:,
929:)
918:D
914:f
907:e
904:R
894:+
885:D
881:/
870:(
847:=
838:D
834:f
828:1
801:D
797:f
772:D
768:/
742:D
738:f
714:.
706:,
702:e
699:R
694:/
687:=
682:D
678:f
648:D
644:f
620:e
617:R
586:D
582:/
552:D
548:f
521:D
501:L
479:D
475:f
454:V
411:,
406:D
403:L
396:2
390:2
386:V
374:D
370:f
366:=
363:p
332:f
328:h
323:g
316:=
313:p
284:;
278:g
274:2
268:2
264:V
256:D
253:L
246:D
242:f
238:=
233:f
229:h
203:D
199:f
172:f
168:h
147:p
105:D
77:D
72:D
68:f
44:D
40:f
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