398:
515:
713:
1251:
1295:
as time-dependent and then applying the derivative product rule. A correct description of such an object requires the application of Newton's second law to the entire, constant-mass system consisting of both the object and its ejected mass.
352:
422:
733:- ignoring the area spanned by the holes in the filter/membrane. The spaces would be cross-sectional areas. For liquids passing through a pipe, the area is the cross-section of the pipe, at the section considered. The
618:
1134:
385:
crossing the boundary for some time duration, not the initial amount of mass at the boundary minus the final amount at the boundary, since the change in mass flowing through the area would be zero for
1159:
1042:
812:
883:
1347:
260:
919:
772:
131:
945:
550:
213:
76:
721:
required to calculate the mass flow rate is real or imaginary, flat or curved, either as a cross-sectional area or a surface, e.g. for substances passing through a
1367:
1061:
1532:
1453:
1419:
1044:
These results are equivalent to the equation containing the dot product. Sometimes these equations are used to define the mass flow rate.
401:
Illustration of volume flow rate. Mass flow rate can be calculated by multiplying the volume flow rate by the mass density of the fluid,
977:
611:
The above equation is only true for a flat, plane area. In general, including cases where the area is curved, the equation becomes a
510:{\displaystyle {\dot {m}}=\rho \cdot {\dot {V}}=\rho \cdot \mathbf {v} \cdot \mathbf {A} =\mathbf {j} _{\text{m}}\cdot \mathbf {A} ,}
1621:
1507:
381:
quantity, the mass flow rate (the time derivative of mass) is also a scalar quantity. The change in mass is the amount that flows
708:{\displaystyle {\dot {m}}=\iint _{A}\rho \mathbf {v} \cdot d\mathbf {A} =\iint _{A}\mathbf {j} _{\text{m}}\cdot d\mathbf {A} .}
1666:
1302:
1047:
Considering flow through porous media, a special quantity, superficial mass flow rate, can be introduced. It is related with
777:
835:
1246:{\displaystyle \rho _{1}\mathbf {v} _{1}\cdot \mathbf {A} _{1}=\rho _{2}\mathbf {v} _{2}\cdot \mathbf {A} _{2}.}
587:
1493:
Lindeburg M. R. Chemical
Engineering Reference Manual for the PE Exam. – Professional Publications (CA), 2013.
1656:
1651:
1424:
1260:
921:
and the velocity of mass elements. The amount passing through the cross-section is reduced by the factor
895:
748:
99:
951:
increases less mass passes through. All mass which passes in tangential directions to the area, that is
1543:
derive a general expression for Newton's second law for variable mass systems by treating the mass in
1429:
1399:
1256:
1048:
557:
370:
92:
31:
1389:
1149:
826:
726:
254:
159:
924:
526:
189:
52:
1502:
Essential
Principles of Physics, P. M. Whelan, M. J. Hodgeson, 2nd Edition, 1978, John Murray,
1259:, such as a rocket ejecting spent fuel. Often, descriptions of such objects erroneously invoke
1627:
1617:
1528:
1503:
1449:
730:
347:{\displaystyle {\dot {m}}=\lim _{\Delta t\to 0}{\frac {\Delta m}{\Delta t}}={\frac {dm}{dt}},}
183:
1466:
612:
405:. The volume flow rate is calculated by multiplying the flow velocity of the mass elements,
378:
1404:
1137:
374:
1480:
1448:
Fluid
Mechanics, M. Potter, D. C. Wiggart, Schaum's Outlines, McGraw Hill (USA), 2008,
1394:
1352:
226:
1661:
1645:
1414:
1153:
952:
737:
is a combination of the magnitude of the area through which the mass passes through,
577:
397:
1255:
In elementary classical mechanics, mass flow rate is encountered when dealing with
722:
179:
155:
17:
818:
742:
734:
590:
386:
230:
175:
143:
1140:
or mass transfer coefficient calculation for fixed and fluidized bed systems.
1631:
1409:
1373:
603:
238:
1377:
1299:
Mass flow rate can be used to calculate the energy flow rate of a fluid:
963:
the area, so the mass passing through the area is zero. This occurs when
729:, the real surface is the (generally curved) surface area of the filter,
163:
567:
139:
82:
167:
718:
151:
1129:{\displaystyle {\dot {m}}_{s}=v_{s}\cdot \rho ={\dot {m}}/A}
250:. In this article, the (more intuitive) definition is used.
171:
1600:
having parts among which there is an interchange of mass.
825:
the cross-section is the amount normal to the area, i.e.
1467:"Mass Flow Rate Fluids Flow Equation - Engineers Edge"
1355:
1305:
1162:
1064:
980:
927:
898:
838:
780:
751:
621:
529:
425:
263:
192:
102:
55:
91:
81:
44:
39:
1361:
1341:
1245:
1128:
1036:
939:
913:
877:
806:
766:
707:
544:
509:
346:
207:
125:
70:
1037:{\displaystyle {\dot {m}}=\rho vA\cos(\pi /2)=0.}
905:
807:{\displaystyle \mathbf {A} =A\mathbf {\hat {n}} }
798:
758:
27:Mass of a substance which passes per unit of time
280:
878:{\displaystyle {\dot {m}}=\rho vA\cos \theta ,}
1614:Thermodynamics : an engineering approach
8:
1612:Çengel, Yunus A.; Boles, Michael A. (2002).
1518:
1516:
221:, pronounced "m-dot"), although sometimes
1354:
1322:
1321:
1307:
1306:
1304:
1234:
1229:
1219:
1214:
1207:
1194:
1189:
1179:
1174:
1167:
1161:
1118:
1107:
1106:
1091:
1078:
1067:
1066:
1063:
1017:
982:
981:
979:
926:
900:
899:
897:
840:
839:
837:
793:
792:
781:
779:
753:
752:
750:
697:
685:
680:
673:
661:
650:
641:
623:
622:
620:
531:
530:
528:
499:
490:
485:
476:
468:
448:
447:
427:
426:
424:
417:Mass flow rate can also be calculated by
321:
298:
283:
265:
264:
262:
194:
193:
191:
112:
104:
103:
101:
57:
56:
54:
396:
1441:
1342:{\displaystyle {\dot {E}}={\dot {m}}e,}
409:, by the cross-sectional vector area,
116:
113:
109:
105:
36:
1616:(4th ed.). Boston: McGraw-Hill.
1420:Standard cubic centimetres per minute
1369:is the unit mass energy of a system.
892:is the angle between the unit normal
821:is as follows. The only mass flowing
7:
236:Sometimes, mass flow rate is termed
1527:. Vol. 1. Wiley. p. 199.
1058:, with the following relationship:
914:{\displaystyle \mathbf {\hat {n}} }
829:to the unit normal. This amount is
767:{\displaystyle \mathbf {\hat {n}} }
248:Schaum's Outline of Fluid Mechanics
126:{\displaystyle {\mathsf {MT^{-1}}}}
309:
301:
284:
25:
1592:to analyze variable mass systems
1372:Energy flow rate has SI units of
253:Mass flow rate is defined by the
1539:It is important to note that we
1230:
1215:
1190:
1175:
902:
795:
782:
755:
698:
681:
662:
651:
500:
486:
477:
469:
358:through a surface per unit time
154:of a substance which passes per
1598:entire system of constant mass
1148:In the elementary form of the
1025:
1011:
290:
1:
1136:The quantity can be used in
940:{\displaystyle \cos \theta }
1683:
1523:Halliday; Resnick (1977).
1283:by treating both the mass
545:{\displaystyle {\dot {V}}}
208:{\displaystyle {\dot {m}}}
71:{\displaystyle {\dot {m}}}
29:
1257:objects of variable mass
1138:particle Reynolds number
186:. The common symbol is
30:Not to be confused with
1425:Thermal mass flow meter
354:i.e., the flow of mass
1363:
1343:
1247:
1130:
1038:
941:
915:
879:
808:
768:
709:
546:
511:
414:
348:
209:
127:
72:
1667:Mechanical quantities
1596:if we apply it to an
1364:
1344:
1248:
1131:
1039:
942:
916:
880:
809:
769:
710:
580:of the mass elements,
547:
512:
400:
393:Alternative equations
349:
210:
128:
73:
1430:Volumetric flow rate
1400:Mass flow controller
1353:
1303:
1160:
1062:
1049:superficial velocity
978:
955:to the unit normal,
925:
896:
836:
778:
749:
745:normal to the area,
619:
527:
423:
261:
190:
100:
53:
32:Volumetric flow rate
1390:Continuity equation
1261:Newton's second law
1150:continuity equation
817:The reason for the
365:The overdot on the
18:Mass flow (physics)
1359:
1339:
1243:
1126:
1034:
937:
911:
875:
804:
774:. The relation is
764:
705:
542:
507:
415:
377:. Since mass is a
344:
297:
246:, see for example
205:
184:US customary units
123:
68:
1534:978-0-471-03710-1
1454:978-0-07-148781-8
1362:{\displaystyle e}
1330:
1315:
1289:and the velocity
1115:
1075:
990:
908:
848:
801:
761:
688:
631:
539:
493:
456:
435:
371:Newton's notation
339:
316:
279:
273:
202:
136:
135:
65:
16:(Redirected from
1674:
1636:
1635:
1609:
1603:
1602:
1520:
1511:
1500:
1494:
1491:
1485:
1484:
1481:"Mass Flow Rate"
1477:
1471:
1470:
1463:
1457:
1446:
1368:
1366:
1365:
1360:
1348:
1346:
1345:
1340:
1332:
1331:
1323:
1317:
1316:
1308:
1294:
1288:
1282:
1252:
1250:
1249:
1244:
1239:
1238:
1233:
1224:
1223:
1218:
1212:
1211:
1199:
1198:
1193:
1184:
1183:
1178:
1172:
1171:
1135:
1133:
1132:
1127:
1122:
1117:
1116:
1108:
1096:
1095:
1083:
1082:
1077:
1076:
1068:
1043:
1041:
1040:
1035:
1021:
992:
991:
983:
973:
946:
944:
943:
938:
920:
918:
917:
912:
910:
909:
901:
884:
882:
881:
876:
850:
849:
841:
813:
811:
810:
805:
803:
802:
794:
785:
773:
771:
770:
765:
763:
762:
754:
714:
712:
711:
706:
701:
690:
689:
686:
684:
678:
677:
665:
654:
646:
645:
633:
632:
624:
613:surface integral
558:volume flow rate
551:
549:
548:
543:
541:
540:
532:
516:
514:
513:
508:
503:
495:
494:
491:
489:
480:
472:
458:
457:
449:
437:
436:
428:
368:
361:
357:
353:
351:
350:
345:
340:
338:
330:
322:
317:
315:
307:
299:
296:
275:
274:
266:
214:
212:
211:
206:
204:
203:
195:
132:
130:
129:
124:
122:
121:
120:
119:
77:
75:
74:
69:
67:
66:
58:
37:
21:
1682:
1681:
1677:
1676:
1675:
1673:
1672:
1671:
1642:
1641:
1640:
1639:
1624:
1611:
1610:
1606:
1535:
1522:
1521:
1514:
1501:
1497:
1492:
1488:
1479:
1478:
1474:
1465:
1464:
1460:
1447:
1443:
1438:
1405:Mass flow meter
1386:
1351:
1350:
1301:
1300:
1290:
1284:
1263:
1228:
1213:
1203:
1188:
1173:
1163:
1158:
1157:
1146:
1087:
1065:
1060:
1059:
1056:
976:
975:
964:
923:
922:
894:
893:
834:
833:
776:
775:
747:
746:
731:macroscopically
679:
669:
637:
617:
616:
609:
601:
588:cross-sectional
525:
524:
484:
421:
420:
395:
375:time derivative
366:
359:
355:
331:
323:
308:
300:
259:
258:
188:
187:
108:
98:
97:
51:
50:
47:
35:
28:
23:
22:
15:
12:
11:
5:
1680:
1678:
1670:
1669:
1664:
1659:
1657:Temporal rates
1654:
1652:Fluid dynamics
1644:
1643:
1638:
1637:
1622:
1604:
1533:
1512:
1495:
1486:
1472:
1458:
1440:
1439:
1437:
1434:
1433:
1432:
1427:
1422:
1417:
1412:
1407:
1402:
1397:
1395:Fluid dynamics
1392:
1385:
1382:
1376:per second or
1358:
1338:
1335:
1329:
1326:
1320:
1314:
1311:
1242:
1237:
1232:
1227:
1222:
1217:
1210:
1206:
1202:
1197:
1192:
1187:
1182:
1177:
1170:
1166:
1145:
1142:
1125:
1121:
1114:
1111:
1105:
1102:
1099:
1094:
1090:
1086:
1081:
1074:
1071:
1054:
1033:
1030:
1027:
1024:
1020:
1016:
1013:
1010:
1007:
1004:
1001:
998:
995:
989:
986:
959:actually pass
936:
933:
930:
907:
904:
886:
885:
874:
871:
868:
865:
862:
859:
856:
853:
847:
844:
800:
797:
791:
788:
784:
760:
757:
704:
700:
696:
693:
683:
676:
672:
668:
664:
660:
657:
653:
649:
644:
640:
636:
630:
627:
608:
607:
599:
594:
581:
571:
561:
538:
535:
521:
506:
502:
498:
488:
483:
479:
475:
471:
467:
464:
461:
455:
452:
446:
443:
440:
434:
431:
394:
391:
343:
337:
334:
329:
326:
320:
314:
311:
306:
303:
295:
292:
289:
286:
282:
278:
272:
269:
201:
198:
182:per second in
178:per second or
148:mass flow rate
134:
133:
118:
115:
111:
107:
95:
89:
88:
85:
79:
78:
64:
61:
48:
46:Common symbols
45:
42:
41:
40:Mass Flow rate
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
1679:
1668:
1665:
1663:
1660:
1658:
1655:
1653:
1650:
1649:
1647:
1633:
1629:
1625:
1623:0-07-238332-1
1619:
1615:
1608:
1605:
1601:
1599:
1595:
1591:
1587:
1584:
1580:
1576:
1572:
1568:
1565:
1561:
1557:
1553:
1550:
1546:
1542:
1536:
1530:
1526:
1519:
1517:
1513:
1509:
1508:0-7195-3382-1
1505:
1499:
1496:
1490:
1487:
1482:
1476:
1473:
1468:
1462:
1459:
1455:
1451:
1445:
1442:
1435:
1431:
1428:
1426:
1423:
1421:
1418:
1416:
1415:Orifice plate
1413:
1411:
1408:
1406:
1403:
1401:
1398:
1396:
1393:
1391:
1388:
1387:
1383:
1381:
1379:
1375:
1370:
1356:
1336:
1333:
1327:
1324:
1318:
1312:
1309:
1297:
1293:
1287:
1281:
1277:
1274:
1270:
1266:
1262:
1258:
1253:
1240:
1235:
1225:
1220:
1208:
1204:
1200:
1195:
1185:
1180:
1168:
1164:
1155:
1154:hydrodynamics
1152:for mass, in
1151:
1143:
1141:
1139:
1123:
1119:
1112:
1109:
1103:
1100:
1097:
1092:
1088:
1084:
1079:
1072:
1069:
1057:
1050:
1045:
1031:
1028:
1022:
1018:
1014:
1008:
1005:
1002:
999:
996:
993:
987:
984:
971:
967:
962:
958:
954:
953:perpendicular
950:
934:
931:
928:
891:
872:
869:
866:
863:
860:
857:
854:
851:
845:
842:
832:
831:
830:
828:
824:
820:
815:
789:
786:
744:
740:
736:
732:
728:
724:
720:
715:
702:
694:
691:
674:
670:
666:
658:
655:
647:
642:
638:
634:
628:
625:
614:
605:
598:
595:
592:
589:
585:
582:
579:
578:flow velocity
575:
572:
570:of the fluid,
569:
565:
562:
559:
555:
536:
533:
523:
522:
520:
517:
504:
496:
481:
473:
465:
462:
459:
453:
450:
444:
441:
438:
432:
429:
418:
412:
408:
404:
399:
392:
390:
388:
384:
380:
376:
372:
363:
341:
335:
332:
327:
324:
318:
312:
304:
293:
287:
276:
270:
267:
256:
251:
249:
245:
241:
240:
234:
232:
228:
224:
220:
219:
199:
196:
185:
181:
177:
173:
169:
165:
161:
157:
153:
149:
145:
141:
96:
94:
90:
86:
84:
80:
62:
59:
49:
43:
38:
33:
19:
1613:
1607:
1597:
1593:
1589:
1585:
1582:
1578:
1574:
1570:
1566:
1563:
1559:
1555:
1551:
1548:
1544:
1540:
1538:
1524:
1498:
1489:
1475:
1461:
1444:
1371:
1298:
1291:
1285:
1279:
1275:
1272:
1268:
1264:
1254:
1147:
1052:
1046:
969:
965:
960:
956:
948:
889:
887:
822:
816:
738:
716:
610:
596:
583:
573:
563:
553:
518:
419:
416:
410:
406:
402:
382:
364:
252:
247:
244:mass current
243:
237:
235:
222:
217:
216:
156:unit of time
147:
137:
83:SI unit
819:dot product
743:unit vector
735:vector area
591:vector area
387:steady flow
233:) is used.
174:units, and
144:engineering
1646:Categories
1436:References
229:lowercase
1410:Mass flux
1374:kilojoule
1328:˙
1313:˙
1226:⋅
1205:ρ
1186:⋅
1165:ρ
1113:˙
1101:ρ
1098:⋅
1073:˙
1015:π
1009:
997:ρ
988:˙
935:θ
932:
906:^
870:θ
867:
855:ρ
846:˙
799:^
759:^
692:⋅
671:∬
656:⋅
648:ρ
639:∬
629:˙
604:mass flux
593:/surface,
537:˙
497:⋅
474:⋅
466:⋅
463:ρ
454:˙
445:⋅
442:ρ
433:˙
310:Δ
302:Δ
291:→
285:Δ
271:˙
239:mass flux
200:˙
114:−
93:Dimension
63:˙
1632:45791449
1571:variable
1384:See also
1378:kilowatt
827:parallel
741:, and a
727:membrane
164:kilogram
1569:) as a
1525:Physics
961:through
957:doesn't
823:through
568:density
566:= mass
158:. Its
150:is the
140:physics
1630:
1620:
1573:. We
1541:cannot
1531:
1506:
1452:
1349:where
888:where
723:filter
519:where
379:scalar
373:for a
168:second
1144:Usage
947:, as
725:or a
383:after
255:limit
227:Greek
180:pound
1662:Mass
1628:OCLC
1618:ISBN
1594:only
1577:use
1529:ISBN
1504:ISBN
1450:ISBN
719:area
717:The
176:slug
166:per
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152:mass
142:and
87:kg/s
1575:can
1006:cos
929:cos
864:cos
552:or
369:is
281:lim
242:or
170:in
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138:In
1648::
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1590:dt
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1380:.
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1278:)/
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389:.
362:.
257::
231:mu
172:SI
146:,
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1273:m
1271:(
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1241:.
1236:2
1231:A
1221:2
1216:v
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1181:1
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1169:1
1124:A
1120:/
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1104:=
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1085:=
1080:s
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1055:s
1053:v
1029:=
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1023:2
1019:/
1012:(
1003:A
1000:v
994:=
985:m
970:π
966:θ
949:θ
903:n
890:θ
873:,
861:A
858:v
852:=
843:m
796:n
790:A
787:=
783:A
756:n
739:A
703:.
699:A
695:d
687:m
682:j
675:A
667:=
663:A
659:d
652:v
643:A
635:=
626:m
606:.
600:m
597:j
584:A
574:v
564:ρ
560:,
554:Q
534:V
505:,
501:A
492:m
487:j
482:=
478:A
470:v
460:=
451:V
439:=
430:m
413:.
411:A
407:v
403:ρ
367:m
360:t
356:m
342:,
336:t
333:d
328:m
325:d
319:=
313:t
305:m
294:0
288:t
277:=
268:m
225:(
223:μ
218:ṁ
215:(
197:m
117:1
110:T
106:M
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