870:, it is common industry practice to reduce the impeller diameter by "trimming", whereby the outer diameter of a particular impeller is reduced by machining to alter the performance of the pump. In this particular industry it is also common to refer to the mathematical approximations that relate the volumetric flow rate, trimmed impeller diameter, shaft rotational speed, developed head, and power as the "affinity laws". Because trimming an impeller changes the fundamental shape of the impeller (increasing the
850:, which is rarely exactly true, but can be a good approximation when used over appropriate frequency or diameter ranges (i.e., a fan will not move anywhere near 1000 times as much air when spun at 1000 times its designed operating speed, but the air movement may be increased by 99% when the operating speed is only doubled). The exact relationship between speed, diameter, and efficiency depends on the particulars of the individual fan or pump design.
25:
124:. The affinity laws are useful as they allow prediction of the head discharge characteristic of a pump or fan from a known characteristic measured at a different speed or impeller diameter. The only requirement is that the two pumps or fans are dynamically similar, that is, the ratios of the fluid forced are the same. It is also required that the two impellers' speed or diameter are running at the same efficiency.
862:
from accurate data is also more accurate than the affinity laws. When applied to pumps, the laws work well for constant diameter variable speed case (Law 1) but are less accurate for constant speed variable impeller diameter case (Law 2).
874:), the relationships shown in Law 2 cannot be utilized in this scenario. In this case, the industry looks to the following relationships, which is a better approximation of these variables when dealing with impeller trimming.
1154:
1063:
968:
678:
587:
496:
400:
309:
218:
848:
1280:
1254:
1228:
1206:
1180:
800:
778:
752:
730:
704:
1074:
983:
888:
598:
507:
416:
320:
229:
138:
1314:
858:
become necessary if the range of acceptability is unknown, or if a high level of accuracy is required in the calculation.
64:
855:
813:
46:
35:
1407:
121:
42:
1231:
755:
878:
With shaft speed (N) held constant and for small variations in impeller diameter via trimming:
1349:
1183:
707:
117:. In these rotary implements, the affinity laws apply both to centrifugal and axial flows.
98:
93:
to express the relationship between variables involved in pump or fan performance (such as
8:
1397:
1325:
1265:
1257:
1239:
1213:
1191:
1165:
974:
785:
763:
737:
715:
689:
1412:
1292:
114:
867:
110:
94:
851:
501:
Law 2b. Pressure or Head is proportional to the square of the impeller diameter:
102:
1402:
871:
1391:
882:
The volumetric flow rate varies directly with the trimmed impeller diameter:
859:
1149:{\displaystyle {P_{1} \over P_{2}}={\left({D_{1} \over D_{2}}\right)^{3}}}
1058:{\displaystyle {H_{1} \over H_{2}}={\left({D_{1} \over D_{2}}\right)^{2}}}
963:{\displaystyle {Q_{1} \over Q_{2}}={\left({D_{1} \over D_{2}}\right)^{1}}}
673:{\displaystyle {P_{1} \over P_{2}}={\left({D_{1} \over D_{2}}\right)^{3}}}
582:{\displaystyle {H_{1} \over H_{2}}={\left({D_{1} \over D_{2}}\right)^{2}}}
491:{\displaystyle {Q_{1} \over Q_{2}}={\left({D_{1} \over D_{2}}\right)^{1}}}
395:{\displaystyle {P_{1} \over P_{2}}={\left({N_{1} \over N_{2}}\right)^{3}}}
304:{\displaystyle {H_{1} \over H_{2}}={\left({N_{1} \over N_{2}}\right)^{2}}}
213:{\displaystyle {Q_{1} \over Q_{2}}={\left({N_{1} \over N_{2}}\right)^{1}}}
81:(also known as the "Fan Laws" or "Pump Laws") for pumps/fans are used in
807:
223:
Law 1b. Pressure or Head is proportional to the square of shaft speed:
82:
780:
is the pressure or head developed by the fan/pump (e.g. psi or Pascal)
86:
592:
Law 2c. Power is proportional to the cube of the impeller diameter:
1068:
The power varies to the cube of the trimmed impeller diameter:
106:
90:
314:
Law 1c. Power is proportional to the cube of shaft speed:
977:) varies to the square of the trimmed impeller diameter:
410:
Law 2a. Flow is proportional to the impeller diameter:
1268:
1242:
1216:
1194:
1168:
1077:
986:
891:
816:
788:
766:
740:
718:
692:
601:
510:
419:
323:
232:
141:
45:. Please help to ensure that disputed statements are
16:
Relationships between equipment performance and power
1274:
1248:
1222:
1200:
1174:
1148:
1057:
962:
842:
794:
772:
746:
724:
698:
672:
581:
490:
394:
303:
212:
1389:
128:Law 1. With impeller diameter (D) held constant:
132:Law 1a. Flow is proportional to shaft speed:
1315:"Basic Pump Parameters and the Affinity Laws"
406:Law 2. With shaft speed (N) held constant:
1372:
1370:
1368:
1366:
1309:
1307:
65:Learn how and when to remove this message
1208:is the impeller diameter (e.g. in or mm)
732:is the impeller diameter (e.g. in or mm)
41:Relevant discussion may be found on the
1390:
1363:
1304:
1260:developed by the pump (e.g. m or ft)
1230:is the shaft rotational speed (e.g.
806:These laws assume that the pump/fan
754:is the shaft rotational speed (e.g.
18:
843:{\displaystyle \eta _{1}=\eta _{2}}
13:
1182:is the volumetric flow rate (e.g.
706:is the volumetric flow rate (e.g.
14:
1424:
1376:
1282:is the shaft power (e.g. W or HP)
23:
1379:Cameron Hydraulic Data, 19th Ed
120:The laws are derived using the
1342:
1:
1298:
973:The pump developed head (the
856:computational fluid dynamics
802:is the shaft power (e.g. W).
7:
1286:
10:
1429:
1276:
1250:
1224:
1202:
1176:
1150:
1059:
964:
844:
810:remains constant i.e.
796:
774:
748:
726:
700:
674:
583:
492:
396:
305:
214:
1277:
1251:
1225:
1203:
1177:
1151:
1060:
965:
845:
797:
775:
749:
727:
701:
675:
584:
493:
397:
306:
215:
1350:"Pump Affinity Laws"
1266:
1240:
1214:
1192:
1166:
1075:
984:
889:
814:
786:
764:
738:
716:
690:
599:
508:
417:
321:
230:
139:
122:Buckingham π theorem
99:volumetric flow rate
34:factual accuracy is
101:, shaft speed) and
1272:
1258:total dynamic head
1246:
1220:
1198:
1172:
1146:
1055:
975:total dynamic head
960:
840:
792:
770:
744:
722:
696:
670:
579:
488:
392:
301:
210:
115:hydraulic turbines
1293:Centripetal force
1275:{\displaystyle P}
1249:{\displaystyle H}
1223:{\displaystyle N}
1201:{\displaystyle D}
1175:{\displaystyle Q}
1133:
1100:
1042:
1009:
947:
914:
868:centrifugal pumps
795:{\displaystyle P}
773:{\displaystyle H}
747:{\displaystyle N}
725:{\displaystyle D}
699:{\displaystyle Q}
657:
624:
566:
533:
475:
442:
379:
346:
288:
255:
197:
164:
75:
74:
67:
1420:
1408:Ventilation fans
1383:
1382:
1381:. pp. 1–30.
1374:
1361:
1360:
1358:
1356:
1346:
1340:
1339:
1337:
1336:
1330:
1324:. Archived from
1319:
1311:
1281:
1279:
1278:
1273:
1255:
1253:
1252:
1247:
1229:
1227:
1226:
1221:
1207:
1205:
1204:
1199:
1181:
1179:
1178:
1173:
1155:
1153:
1152:
1147:
1145:
1144:
1143:
1138:
1134:
1132:
1131:
1122:
1121:
1112:
1101:
1099:
1098:
1089:
1088:
1079:
1064:
1062:
1061:
1056:
1054:
1053:
1052:
1047:
1043:
1041:
1040:
1031:
1030:
1021:
1010:
1008:
1007:
998:
997:
988:
969:
967:
966:
961:
959:
958:
957:
952:
948:
946:
945:
936:
935:
926:
915:
913:
912:
903:
902:
893:
866:For radial flow
849:
847:
846:
841:
839:
838:
826:
825:
801:
799:
798:
793:
779:
777:
776:
771:
753:
751:
750:
745:
731:
729:
728:
723:
705:
703:
702:
697:
679:
677:
676:
671:
669:
668:
667:
662:
658:
656:
655:
646:
645:
636:
625:
623:
622:
613:
612:
603:
588:
586:
585:
580:
578:
577:
576:
571:
567:
565:
564:
555:
554:
545:
534:
532:
531:
522:
521:
512:
497:
495:
494:
489:
487:
486:
485:
480:
476:
474:
473:
464:
463:
454:
443:
441:
440:
431:
430:
421:
401:
399:
398:
393:
391:
390:
389:
384:
380:
378:
377:
368:
367:
358:
347:
345:
344:
335:
334:
325:
310:
308:
307:
302:
300:
299:
298:
293:
289:
287:
286:
277:
276:
267:
256:
254:
253:
244:
243:
234:
219:
217:
216:
211:
209:
208:
207:
202:
198:
196:
195:
186:
185:
176:
165:
163:
162:
153:
152:
143:
105:. They apply to
70:
63:
59:
56:
50:
47:reliably sourced
27:
26:
19:
1428:
1427:
1423:
1422:
1421:
1419:
1418:
1417:
1388:
1387:
1386:
1375:
1364:
1354:
1352:
1348:
1347:
1343:
1334:
1332:
1328:
1317:
1313:
1312:
1305:
1301:
1289:
1267:
1264:
1263:
1241:
1238:
1237:
1215:
1212:
1211:
1193:
1190:
1189:
1167:
1164:
1163:
1139:
1127:
1123:
1117:
1113:
1111:
1107:
1106:
1105:
1094:
1090:
1084:
1080:
1078:
1076:
1073:
1072:
1048:
1036:
1032:
1026:
1022:
1020:
1016:
1015:
1014:
1003:
999:
993:
989:
987:
985:
982:
981:
953:
941:
937:
931:
927:
925:
921:
920:
919:
908:
904:
898:
894:
892:
890:
887:
886:
852:Product testing
834:
830:
821:
817:
815:
812:
811:
787:
784:
783:
765:
762:
761:
739:
736:
735:
717:
714:
713:
691:
688:
687:
663:
651:
647:
641:
637:
635:
631:
630:
629:
618:
614:
608:
604:
602:
600:
597:
596:
572:
560:
556:
550:
546:
544:
540:
539:
538:
527:
523:
517:
513:
511:
509:
506:
505:
481:
469:
465:
459:
455:
453:
449:
448:
447:
436:
432:
426:
422:
420:
418:
415:
414:
385:
373:
369:
363:
359:
357:
353:
352:
351:
340:
336:
330:
326:
324:
322:
319:
318:
294:
282:
278:
272:
268:
266:
262:
261:
260:
249:
245:
239:
235:
233:
231:
228:
227:
203:
191:
187:
181:
177:
175:
171:
170:
169:
158:
154:
148:
144:
142:
140:
137:
136:
71:
60:
54:
51:
40:
32:This article's
28:
24:
17:
12:
11:
5:
1426:
1416:
1415:
1410:
1405:
1400:
1385:
1384:
1362:
1341:
1302:
1300:
1297:
1296:
1295:
1288:
1285:
1284:
1283:
1271:
1261:
1245:
1235:
1219:
1209:
1197:
1187:
1171:
1157:
1156:
1142:
1137:
1130:
1126:
1120:
1116:
1110:
1104:
1097:
1093:
1087:
1083:
1066:
1065:
1051:
1046:
1039:
1035:
1029:
1025:
1019:
1013:
1006:
1002:
996:
992:
971:
970:
956:
951:
944:
940:
934:
930:
924:
918:
911:
907:
901:
897:
872:specific speed
837:
833:
829:
824:
820:
804:
803:
791:
781:
769:
759:
743:
733:
721:
711:
695:
681:
680:
666:
661:
654:
650:
644:
640:
634:
628:
621:
617:
611:
607:
590:
589:
575:
570:
563:
559:
553:
549:
543:
537:
530:
526:
520:
516:
499:
498:
484:
479:
472:
468:
462:
458:
452:
446:
439:
435:
429:
425:
403:
402:
388:
383:
376:
372:
366:
362:
356:
350:
343:
339:
333:
329:
312:
311:
297:
292:
285:
281:
275:
271:
265:
259:
252:
248:
242:
238:
221:
220:
206:
201:
194:
190:
184:
180:
174:
168:
161:
157:
151:
147:
73:
72:
31:
29:
22:
15:
9:
6:
4:
3:
2:
1425:
1414:
1411:
1409:
1406:
1404:
1401:
1399:
1396:
1395:
1393:
1380:
1373:
1371:
1369:
1367:
1351:
1345:
1331:on 2016-03-03
1327:
1323:
1316:
1310:
1308:
1303:
1294:
1291:
1290:
1269:
1262:
1259:
1243:
1236:
1233:
1217:
1210:
1195:
1188:
1186:, GPM or L/s)
1185:
1169:
1162:
1161:
1160:
1140:
1135:
1128:
1124:
1118:
1114:
1108:
1102:
1095:
1091:
1085:
1081:
1071:
1070:
1069:
1049:
1044:
1037:
1033:
1027:
1023:
1017:
1011:
1004:
1000:
994:
990:
980:
979:
978:
976:
954:
949:
942:
938:
932:
928:
922:
916:
909:
905:
899:
895:
885:
884:
883:
880:
879:
875:
873:
869:
864:
861:
860:Interpolation
857:
853:
835:
831:
827:
822:
818:
809:
789:
782:
767:
760:
757:
741:
734:
719:
712:
710:, GPM or L/s)
709:
693:
686:
685:
684:
664:
659:
652:
648:
642:
638:
632:
626:
619:
615:
609:
605:
595:
594:
593:
573:
568:
561:
557:
551:
547:
541:
535:
528:
524:
518:
514:
504:
503:
502:
482:
477:
470:
466:
460:
456:
450:
444:
437:
433:
427:
423:
413:
412:
411:
408:
407:
386:
381:
374:
370:
364:
360:
354:
348:
341:
337:
331:
327:
317:
316:
315:
295:
290:
283:
279:
273:
269:
263:
257:
250:
246:
240:
236:
226:
225:
224:
204:
199:
192:
188:
182:
178:
172:
166:
159:
155:
149:
145:
135:
134:
133:
130:
129:
125:
123:
118:
116:
112:
108:
104:
100:
96:
92:
88:
84:
80:
79:affinity laws
69:
66:
58:
48:
44:
38:
37:
30:
21:
20:
1378:
1377:Heald, C.C.
1353:. Retrieved
1344:
1333:. Retrieved
1326:the original
1321:
1158:
1067:
972:
881:
877:
876:
865:
805:
682:
591:
500:
409:
405:
404:
313:
222:
131:
127:
126:
119:
78:
76:
61:
52:
33:
1355:18 November
1398:Hydraulics
1392:Categories
1335:2014-06-17
1322:PDH Online
1299:References
808:efficiency
83:hydraulics
832:η
819:η
87:hydronics
43:talk page
1413:Turbines
1287:See also
55:May 2019
36:disputed
1256:is the
1159:where
683:where
89:and/or
113:, and
1403:Pumps
1329:(PDF)
1318:(PDF)
107:pumps
103:power
1357:2014
111:fans
95:head
91:HVAC
77:The
1232:rpm
1184:CFM
854:or
756:rpm
708:CFM
1394::
1365:^
1320:.
1306:^
109:,
97:,
85:,
1359:.
1338:.
1270:P
1244:H
1234:)
1218:N
1196:D
1170:Q
1141:3
1136:)
1129:2
1125:D
1119:1
1115:D
1109:(
1103:=
1096:2
1092:P
1086:1
1082:P
1050:2
1045:)
1038:2
1034:D
1028:1
1024:D
1018:(
1012:=
1005:2
1001:H
995:1
991:H
955:1
950:)
943:2
939:D
933:1
929:D
923:(
917:=
910:2
906:Q
900:1
896:Q
836:2
828:=
823:1
790:P
768:H
758:)
742:N
720:D
694:Q
665:3
660:)
653:2
649:D
643:1
639:D
633:(
627:=
620:2
616:P
610:1
606:P
574:2
569:)
562:2
558:D
552:1
548:D
542:(
536:=
529:2
525:H
519:1
515:H
483:1
478:)
471:2
467:D
461:1
457:D
451:(
445:=
438:2
434:Q
428:1
424:Q
387:3
382:)
375:2
371:N
365:1
361:N
355:(
349:=
342:2
338:P
332:1
328:P
296:2
291:)
284:2
280:N
274:1
270:N
264:(
258:=
251:2
247:H
241:1
237:H
205:1
200:)
193:2
189:N
183:1
179:N
173:(
167:=
160:2
156:Q
150:1
146:Q
68:)
62:(
57:)
53:(
49:.
39:.
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