This paper is a historical review of the science, both experimental and theoretical, behind the iconic Moody diagram used to avoid tedious iterations choosing pumps and pipes. The large body of historical pipe flow measurements and the choice of dimensionless groups and the Buckingham-Π theorem are also discussed. The traditional use of the Moody diagram to solve common pipe flow problem is discussed. Alternatives to the Moody diagram from the literature and novel ones presented here are shown to produce a solution without iteration for any type of pipe loss problem.
Issue Section:
Review Article
References
1.
White
, F. M.
, 2010
, Fluid Mechanics
, 7th ed., McGraw-Hill
, New York
.2.
Lamb
, H.
, 1945
, Hydrodynamics
(Dover Books on Physics), Dover, New York.3.
Schlichting
, H.
, 1975
, Boundary Layer Theory
, 7th ed., McGraw-Hill
, New York.4.
Bridgman
, P. W.
, 1922
, Dimensional Analysis
, Yale University Press
, New Haven, CT.5.
Ruzicka
, M
., 2008
, “On Dimensionless Numbers
,” Chem. Eng. Res. Des.
, 86
(8
), pp. 835
–868
.6.
Newton
, I.
, Cohen
, B.
, Whitman
, A.
, and Budenz
, J.
, 1999
, The Principia: Mathematical Principles of Natural Philosophy
, University of California Press
, Berkeley, CA.7.
Navier
, M.
, 1823
, “Mémoire sur les lois du Mouvement des Fluides
,” Mém. Acad. Sci. Inst. France
, 6
, pp. 389
–440
.8.
Poisson
, M.
, 1831
, “Mémoire Sur les Équations Générales de L’équilibre et du Mouvement des Corps Solides, Élastiques et Fluides
,” J. Éc. Polytech.
, 13
, pp. 1
–174
.9.
Saint-Venant
, B.
, 1843
, “Note à Joindre à un Mémoire Précédemment Présenté sur la Dynamique des Fluides
,” C. R. Hebd. Séances Acad. Sci.
, 17
, pp. 1240
–1243
.10.
Stokes
, G. G.
, 1845
, “On the Theories of the Internal Friction of Fluids in Motion, and of the Equilibrium and Motion of Elastic Solids
,” Trans. Cambridge Philos. Soc.
, 8
, pp. 287
–319
.11.
Maidment
, D.
, 1993
, Handbook of Hydrology
(Civil Engineering), McGraw-Hill
, New York.12.
Kestin
, J.
, Sokolov
, M.
, and Wakeham
, W. A.
, 1978
, “Viscosity of Liquid Water in the Range–8 °C to 150 °C
,” J. Phys. Chem. Ref. Data
, 7
(3
), pp. 941
–948
.13.
Sutherland
, W
., 1893
, “The Viscosity of Gases and Molecular Force
,” London
, Edinburgh Dublin Philos. Mag. J. Sci., 5
(36
), pp. 507
–531
.14.
McKeon
, B. J.
, Swanson
, C. J.
, Zagarola
, M. V.
, Donnelly
, R. J.
, and Smits
, A. J.
, 2004
, “Friction Factors for Smooth Pipe Flow
,” J. Fluid Mech.
, 511
(7
), pp. 41
–44
.15.
Bernoulli
, D.
, 1738
, Hydrodynamica
, Johann Reinhold Dulsecker
, Strasbourg, France.16.
Mikhailov
, G.
, 2005
, “Chapter 9—Daniel Bernoulli, Hydrodynamica (1738)
,” Landmark Writings in Western Mathematics 1640–1940
, I.
Grattan-Guinness
, R.
Cooke
, L.
Corry
, P.
Crépel
, and N.
Guicciardini
, eds., Elsevier Science
, Amsterdam, The Netherlands
, pp. 131
–142
.17.
Euler
, L.
, 1757
, “Principes Généraux de L’état D’équilibre d'un Fluide
,” Mémoires
, Vol. 11
, Académie Royale des Sciences et des Belles-Lettres de Berlin
, Berlin, pp. 217
–273
.18.
de Prony
, R.
, 1825
, Recueil de Cinq Tables
, L'imprimerie Royale
, Paris
.19.
du Buat
, P. L. G.
, 1786
, Principes D'hydraulique: Vérifiés par un Grand Nombre D'expériences Faites par Ordre du Gouvernment…
, Vol. 2
, De l'imprimerie de Monsieur
.20.
Bossut
, C.
, 1787
, Traité Théorique et Expérimental D'hydrodynamique
, Vol. 2
, Imprimerie Royale
, Paris
.21.
Couplet des Tortreaux
, P.
, 1735
, “Recherches sur le Mouvement des Eaux
,” Histoire de l'Académie Royale des Sciences
, A. Royale des Sciences (France)
, ed., Imprimerie Royale
, Paris
, pp. 113
–168
.22.
Poiseuille
, J.
, 1840
, “Recherches Experimentelles sur le Mouvement des Liquides Dans les Tubes de très Petits Diamètres
,” Mémoires présentés par Divers Savants à l'Académie Royale des sciences de l'Institut de France, 9, pp. 433–544.23.
Helmholtz
, H.
, and von Piotrowski
, G.
, 1860
, “Über Reibung Tropfbarer Flüssigkeiten
,” Sitzungsber. Math. Naturw. Classe Kaiserl. Akad. der Wiss. Besonders Abgedruckt
, 40
(1860
), pp. 607
–658
.24.
Reynolds
, O
., 1883
, “An Experimental Investigation of the Circumstances Which Determine Whether the Motion of Water Shall Be Direct or Sinuous, and of the Law of Resistance in Parallel Channels
,” Philos. Trans. R. Soc. London
, 174
(0
), pp. 935
–982
.25.
Hagen
, G. H. L.
, 1839
, “Über die Bewegung des Wassers in Engen Zylindrischen Röhren
,” Annal. Phys. Chem.
, 122
(3
), pp. 423
–442
.26.
Tietjens
, O.
, 1931
, Hydro- und Aeromechanik, nach Vorlesungen von L. Prandtl
, Vol. 2
, Springer Verlag
, Berlin.27.
Tietjens
, O.
, 1957
, Applied Hydro- and Aeromechanics: Based on Lectures of L. Prandtl
, Dover Publications
, New York.28.
Hagen
, G.
, 1854
, “Über den Einfluss der Temperatur auf die Bewegung des Wassers in Röhren
,” Mathematische Abhandlungen Königlichen Akademie der Wissenschaften zu Berlin
, pp. 17
–98
.29.
Weisbach
, J.
, 1845
, Lehrbuch der Ingenieur- und Maschinen-Mechanik
, Friedrich Vieweg und Sohn
, Braunschwieg, Germany
.30.
Weisbach
, J.
, 1848
, Principles of the Mechanics of Machinery and Engineering
, Lea and Blanchard, Philidelphia, PA.31.
Darcy
, H.
, 1856
, Les Fontaines Publiques de la Ville de Dijon
, Dalmont
, Paris
.32.
Rouse
, H.
, 1943
, “Evaluation of Boundary Roughness
,” Second Hydraulics Conference
, Iowa Institute of Hydraulic Research, pp. 105–116.33.
Moody
, L. F.
, 1944
, “Friction Factors for Pipe Flow
,” Trans. ASME
, 66
, pp. 671–684.34.
Stanton
, T. E.
, and Pannell
, J. R.
, 1914
, “Similarity of Motion in Relation to the Surface Friction of Fluids
,” Proc. R. Soc. London Ser. A
, 90
(619
), pp. 394
–395
.35.
Van Dyke
, M.
, 1982
, An Album of Fluid Motion
, Parabolic Press
, Stanford, CA.36.
Mills
, H
., 1924
, “Flow of Water in Pipes
,” Mem. Am. Acad. Arts Sci.
, 15
(2
), pp. 81
–236
.37.
Freeman
, J.
, and Freeman
, C.
, 1941
, “Experiments Upon the Flow of Water in Pipes and Pipe Fittings: Made at Nashua, New Hampshire
, June 28 to Oct. 22, 1892,” The American Society of Mechanical Engineers, New York.38.
Saph
, A. V.
, and Schoder
, E. W.
, 1903
, “An Experimental Study of the Resistances to the Flow of Water in Pipes
,” Trans. Am. Soc. Civil Eng.
, 51
(2
), pp. 253
–312
.39.
Rayleigh
, L.
, 1915
, “The Principle of Similitude
,” Nature
, 95
(2368
), pp. 66
–68
.40.
Rott
, N.
, 1992
, “Lord Rayleigh and Hydrodynamic Similarity
,” Phys. Fluids A: Fluid Dyn.
, 4
(12
), pp. 2595
–2600
.41.
Buckingham
, E
., 1914
, “On Physically Similar Systems; Illustrations of the Use of Dimensional Equations
,” Phys. Rev.
, 4
(4
), pp. 345
–376
.42.
Macagno
, E. O.
, 1971
, “Historico-Critical Review of Dimensional Analysis
,” J. Franklin Inst.
, 292
(6
), pp. 391
–402
.43.
Buckingham
, E
., 1924
, “Dimensional Analysis
,” Philos. Mag. Ser. 6
, 48
(283
), pp. 141
–145
.44.
Blasius
, H.
, 1912
, “Das Aehnlichkeitsgesetz bei Reibungsvorgängen in Flussigkeiten
,” Mitt. Forschungsarb. Gebiete Ingenieurwes.
, 131
, pp. 1–39.45.
Blasius
, H.
, 1912
, “Das Aehnlichkeitsgesetz bei Reibungsvorgängen
,” Zeischrift des Vereines deutscher Ingenieure
, 56
(11
), pp. 639
–643
.46.
Stanton
, T. E.
, 1911
, “The Mechanical Viscosity of Fluids
,” Proc. R. Soc. London. Ser. A
, 85
(579
), pp. 366
–376
.47.
Rayleigh
, L.
, 1910
, “Note as to the Application of the Principle of Dynamical Similarity
,” Advisory Committee on Aeronautics, Reports and Memoranda No. 15.48.
Scobey
, F.
, 1926
, “The Flow of Water in Wood-Stave Pipe
,” Bureau of Public Roads, Washington, DC, Technical Report No. 376.49.
Prandtl
, L.
, 1927
, Über den Reibungswiderstand Strömender Luft
(Ergebnisse der Aerodynamischen Versuchsanstalt zu Göttingen, Vol. 3), Oldenbourg, Munich, Germany.50.
von Kármán
, T.
, 1921
, “Über Laminare und Turbulente Reibung
,” ZAMM J. Appl. Math. Mech.
, 1
(4
), pp. 233
–252
.51.
von Kármán
, T.
, 1946
, “On Laminar and Turbulent Friction
,” NACA Technical Memorandum 1092
.52.
Nikuradse
, J.
, 1932
, “Gesetzmässigkeiten der Turbulenten Strömung in Glatten Rohren
,” VDI Forschungsh.: Beil. Forsch. Geb. Ingenieurwes.
, 356
, pp. 1
–36
.53.
Nikuradse
, J.
, 1966
, “Laws of Turbulent Flow in Smooth Pipes
,” NACA Technical Translation F-10359.54.
Nikuradse
, J.
, 1933
, “Strömungsgesetze in Rauhen Rohren
,” VDI Forschungsh.: Beil. Forsch. Geb. Ingenieurwes.
, 361
, pp. 1–33.55.
Nikuradse
, J.
, 1950
, “Law of Flow in Rough Pipes
,” NACA Technical Memorandum, Report No. 1292
.56.
Beattie
, D. R. H.
, 1995
, “In Defence of Nikuradse
,” 12th Australasian Fluid Mechanics Conference
, pp. 561
–564
.57.
Brownlie
, W. R.
, 1981
, “Re-Examination of Nikuradse Roughness Data
,” J. Hydraul. Div., ASCE
, 107
(1
), pp. 115
–119
.58.
Gad-el-Hak
, M.
, 2001
, The MEMS Handbook
(Mechanical and Aerospace Engineering Series), Vol. 1
, CRC Press
, Boca Raton, FL.59.
Wiedemann
, G.
, 1856
, “Über die Bewegung der Flüssigkeiten im Kreise der Geschlossenen Galvanischen Säule und Ihre Beziehungen zur Elektrolyse
,” Annal. Phys. Chem.
, 99
, pp. 177–233.60.
Hagenbach
, 1860
, “Über die Bestimmung der Zähigkeit einer Flüssigkeit durch den Ausfluss aus Röhren
,” Annal. Phys. Chem.
, 109
, pp. 385–426.61.
Colebrook
, C.
, 1939
, “Turbulent Flow in Pipes, With Particular Reference to Transition Region Between Smooth and Rough Pipe Laws
,” J. Inst. Civil Eng. London
, 11
, pp. 133–156.62.
Brkić
, D.
, 2011
, “Review of Explicit Approximations to the Colebrook Relation for Flow Friction
,” J. Pet. Sci. Eng.
, 77
(1
), pp. 34
–48
.63.
Kalinske
, A.
, 1939
, “A New Method of Presenting Data on Fluid Flow in Pipes
,” Civil Eng.
, 9
(5), p. 313.64.
Schlichting
, H.
, and Gersten
, K.
, 2000
, Boundary Layer Theory
, 8th ed., Springer
, Berlin.65.
Rouse
, H.
, 1976
, Hydraulics in the United States 1776–1976
, Iowa Institute of Hydraulic Research
, Iowa City, IA.66.
Asthana
, K. C.
, 1974
, “Transformation of Moody Diagram
,” J. Hydraul. Div., ASCE
, 100
(6
), pp. 797
–808
.67.
Debler
, W.
, 1977
, “Pipe Sizes From Modified Moody Diagram
,” J. Hydraul. Div., ASCE
, 103
(1
), pp. 81
–85
.68.
Lai
, R. Y. S.
, and Lee
, K. K.
, 1975
, “Moody Diagram for Direct Pipe Diameter Calculation
,” J. Hydraul. Div., ASCE
, 101
(10
), pp. 1377
–1380
.69.
Engineering Department
, 2009
, “Flow of Fluids Through Valves, Resistance and. Pipes, Technical Publication 410
,” Crane
, Stamford, CT
.70.
Idelchik
, I. E.
, 2008
, Handbook of Hydraulic Resistance
, 4th ed. Revised and Augmented, Begell House
, Redding, CT
.71.
Acton
, F. S.
, 1990
, Numerical Methods That Usually Work
, The Mathematical Association of America
, Washington, D.C
.Copyright © 2017 by ASME
You do not currently have access to this content.
