Knowledge (XXG)

Morton number

Source 📝

455: 153: 349: 645: 518: 638: 594: 245: 1000: 631: 218: 187: 377: 265: 69: 654: 277: 561: 990: 800: 466: 532: 19: 995: 47:
or Bond number to characterize the shape of bubbles or drops moving in a surrounding fluid or continuous phase,
877: 860: 271:
coefficient. For the case of a bubble with a negligible inner density the Morton number can be simplified to
1005: 855: 755: 715: 710: 40: 780: 750: 690: 227: 44: 964: 450:{\displaystyle \mathrm {Mo} ={\frac {\mathrm {We} ^{3}}{\mathrm {Fr} ^{2}\,\mathrm {Re} ^{4}}}.} 196: 919: 884: 665: 557: 165: 148:{\displaystyle \mathrm {Mo} ={\frac {g\mu _{c}^{4}\,\Delta \rho }{\rho _{c}^{2}\sigma ^{3}}},} 250: 969: 845: 840: 825: 790: 700: 609: 579:
An experimental investigation of the drag and shape of air bubbles rising in various liquids
623: 613: 18:
This article is about fluid mechanics. For the linear ordering of points in the plane, see
934: 914: 872: 867: 695: 368: 268: 944: 924: 909: 904: 850: 835: 810: 805: 795: 775: 765: 730: 675: 28: 984: 954: 949: 939: 929: 894: 889: 770: 760: 740: 735: 705: 670: 577: 364: 959: 899: 815: 785: 745: 720: 680: 360: 820: 725: 685: 52: 344:{\displaystyle \mathrm {Mo} ={\frac {g\mu _{c}^{4}}{\rho _{c}\sigma ^{3}}}.} 190: 595:"History and significance of the Morton number in hydraulic engineering" 221: 359:
The Morton number can also be expressed by using a combination of the
627: 582:, Report 802, Navy Department: The David W. Taylor Model Basin 460:
The Froude number in the above expression is defined as
513:{\displaystyle \mathrm {Fr^{2}} ={\frac {V^{2}}{gd}}} 469: 380: 280: 253: 230: 199: 168: 72: 512: 449: 343: 259: 239: 212: 181: 147: 55:, who described it with W. L. Haberman in 1953. 593:Pfister, Michael; Hager, Willi H. (May 2014). 552:Clift, R.; Grace, J. R.; Weber, M. E. (1978), 639: 247:the difference in density of the phases, and 8: 646: 632: 624: 494: 488: 478: 470: 468: 435: 427: 425: 419: 411: 403: 395: 392: 381: 379: 329: 319: 307: 302: 292: 281: 279: 252: 229: 204: 198: 173: 167: 133: 123: 118: 105: 99: 94: 84: 73: 71: 1001:Dimensionless numbers of fluid mechanics 655:Dimensionless numbers in fluid mechanics 576:Haberman, W. L.; Morton, R. K. (1953), 544: 7: 614:10.1061/(asce)hy.1943-7900.0000870 475: 471: 431: 428: 415: 412: 399: 396: 385: 382: 285: 282: 231: 106: 77: 74: 14: 602:Journal of Hydraulic Engineering 162:is the acceleration of gravity, 63:The Morton number is defined as 1: 20:Morton number (number theory) 556:, New York: Academic Press, 527:is a reference velocity and 355:Relation to other parameters 240:{\displaystyle \Delta \rho } 554:Bubbles Drops and Particles 1022: 224:of the surrounding fluid, 193:of the surrounding fluid, 17: 661: 213:{\displaystyle \rho _{c}} 182:{\displaystyle \mu _{c}} 535:of the drop or bubble. 260:{\displaystyle \sigma } 43:used together with the 514: 451: 345: 261: 241: 214: 183: 149: 991:Dimensionless numbers 515: 452: 346: 262: 242: 215: 184: 150: 467: 378: 278: 251: 228: 197: 166: 70: 51:. It is named after 41:dimensionless number 533:equivalent diameter 312: 128: 104: 801:Keulegan–Carpenter 510: 447: 341: 298: 257: 237: 210: 179: 145: 114: 90: 996:Bubbles (physics) 978: 977: 563:978-0-12-176950-5 508: 442: 336: 140: 1013: 648: 641: 634: 625: 618: 617: 599: 590: 584: 583: 573: 567: 566: 549: 519: 517: 516: 511: 509: 507: 499: 498: 489: 484: 483: 482: 456: 454: 453: 448: 443: 441: 440: 439: 434: 424: 423: 418: 408: 407: 402: 393: 388: 350: 348: 347: 342: 337: 335: 334: 333: 324: 323: 313: 311: 306: 293: 288: 266: 264: 263: 258: 246: 244: 243: 238: 219: 217: 216: 211: 209: 208: 188: 186: 185: 180: 178: 177: 154: 152: 151: 146: 141: 139: 138: 137: 127: 122: 112: 103: 98: 85: 80: 1021: 1020: 1016: 1015: 1014: 1012: 1011: 1010: 981: 980: 979: 974: 657: 652: 622: 621: 608:(5): 02514001. 597: 592: 591: 587: 575: 574: 570: 564: 551: 550: 546: 541: 500: 490: 474: 465: 464: 426: 410: 409: 394: 376: 375: 369:Reynolds number 357: 325: 315: 314: 294: 276: 275: 269:surface tension 249: 248: 226: 225: 200: 195: 194: 169: 164: 163: 129: 113: 86: 68: 67: 61: 23: 12: 11: 5: 1019: 1017: 1009: 1008: 1006:Fluid dynamics 1003: 998: 993: 983: 982: 976: 975: 973: 972: 967: 962: 957: 952: 947: 942: 937: 932: 927: 922: 917: 912: 907: 902: 897: 892: 887: 882: 881: 880: 870: 865: 864: 863: 858: 848: 843: 838: 833: 828: 823: 818: 813: 808: 803: 798: 793: 788: 783: 778: 773: 768: 763: 758: 753: 748: 743: 738: 733: 728: 723: 718: 713: 708: 703: 698: 693: 688: 683: 678: 673: 668: 662: 659: 658: 653: 651: 650: 643: 636: 628: 620: 619: 585: 568: 562: 543: 542: 540: 537: 521: 520: 506: 503: 497: 493: 487: 481: 477: 473: 458: 457: 446: 438: 433: 430: 422: 417: 414: 406: 401: 398: 391: 387: 384: 356: 353: 352: 351: 340: 332: 328: 322: 318: 310: 305: 301: 297: 291: 287: 284: 256: 236: 233: 207: 203: 176: 172: 156: 155: 144: 136: 132: 126: 121: 117: 111: 108: 102: 97: 93: 89: 83: 79: 76: 60: 57: 29:fluid dynamics 25: 24: 13: 10: 9: 6: 4: 3: 2: 1018: 1007: 1004: 1002: 999: 997: 994: 992: 989: 988: 986: 971: 968: 966: 963: 961: 958: 956: 953: 951: 948: 946: 943: 941: 938: 936: 933: 931: 928: 926: 923: 921: 918: 916: 913: 911: 908: 906: 903: 901: 898: 896: 893: 891: 888: 886: 883: 879: 876: 875: 874: 871: 869: 866: 862: 859: 857: 854: 853: 852: 849: 847: 844: 842: 839: 837: 834: 832: 829: 827: 824: 822: 819: 817: 814: 812: 809: 807: 804: 802: 799: 797: 794: 792: 789: 787: 784: 782: 779: 777: 774: 772: 769: 767: 764: 762: 759: 757: 754: 752: 749: 747: 744: 742: 739: 737: 734: 732: 729: 727: 724: 722: 719: 717: 714: 712: 711:Chandrasekhar 709: 707: 704: 702: 699: 697: 694: 692: 689: 687: 684: 682: 679: 677: 674: 672: 669: 667: 664: 663: 660: 656: 649: 644: 642: 637: 635: 630: 629: 626: 615: 611: 607: 603: 596: 589: 586: 581: 580: 572: 569: 565: 559: 555: 548: 545: 538: 536: 534: 530: 526: 504: 501: 495: 491: 485: 479: 463: 462: 461: 444: 436: 420: 404: 389: 374: 373: 372: 370: 366: 365:Froude number 362: 354: 338: 330: 326: 320: 316: 308: 303: 299: 295: 289: 274: 273: 272: 270: 254: 234: 223: 205: 201: 192: 174: 170: 161: 142: 134: 130: 124: 119: 115: 109: 100: 95: 91: 87: 81: 66: 65: 64: 58: 56: 54: 50: 46: 45:Eötvös number 42: 38: 34: 33:Morton number 30: 21: 16: 15: 830: 605: 601: 588: 578: 571: 553: 547: 528: 524: 522: 459: 361:Weber number 358: 159: 157: 62: 48: 36: 32: 26: 965:Weissenberg 53:Rose Morton 985:Categories 885:Richardson 666:Archimedes 539:References 59:Definition 970:Womersley 861:turbulent 841:Ohnesorge 826:Marangoni 791:Iribarren 716:Damköhler 701:Capillary 327:σ 317:ρ 300:μ 255:σ 235:ρ 232:Δ 202:ρ 191:viscosity 171:μ 131:σ 116:ρ 110:ρ 107:Δ 92:μ 945:Suratman 935:Strouhal 915:Sherwood 878:magnetic 873:Reynolds 868:Rayleigh 856:magnetic 696:Brinkman 925:Stanton 920:Shields 910:Scruton 905:Schmidt 851:Prandtl 836:Nusselt 811:Laplace 806:Knudsen 796:Kapitza 781:Görtler 776:Grashof 766:Galilei 731:Deborah 676:Bagnold 531:is the 267:is the 222:density 189:is the 39:) is a 955:Ursell 950:Taylor 940:Stuart 930:Stokes 895:Rossby 890:Roshko 846:Péclet 831:Morton 771:Graetz 761:Froude 751:Eötvös 741:Eckert 736:Dukhin 706:Cauchy 671:Atwood 560:  523:where 158:where 31:, the 960:Weber 900:Rouse 816:Lewis 786:Hagen 756:Euler 746:Ekman 721:Darcy 681:Bejan 598:(PDF) 821:Mach 726:Dean 691:Bond 686:Biot 558:ISBN 367:and 220:the 610:doi 606:140 27:In 987:: 604:. 600:. 371:, 363:, 37:Mo 647:e 640:t 633:v 616:. 612:: 529:d 525:V 505:d 502:g 496:2 492:V 486:= 480:2 476:r 472:F 445:. 437:4 432:e 429:R 421:2 416:r 413:F 405:3 400:e 397:W 390:= 386:o 383:M 339:. 331:3 321:c 309:4 304:c 296:g 290:= 286:o 283:M 206:c 175:c 160:g 143:, 135:3 125:2 120:c 101:4 96:c 88:g 82:= 78:o 75:M 49:c 35:( 22:.

Index

Morton number (number theory)
fluid dynamics
dimensionless number
Eötvös number
Rose Morton
viscosity
density
surface tension
Weber number
Froude number
Reynolds number
equivalent diameter
ISBN
978-0-12-176950-5
An experimental investigation of the drag and shape of air bubbles rising in various liquids
"History and significance of the Morton number in hydraulic engineering"
doi
10.1061/(asce)hy.1943-7900.0000870
v
t
e
Dimensionless numbers in fluid mechanics
Archimedes
Atwood
Bagnold
Bejan
Biot
Bond
Brinkman
Capillary

Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.