Everything you did (not) want to know about the Darcy-Weisbach Equation

1. Everything you did (not) want to know about the Darcy-Weisbach Equation ENSC 3233 Oklahoma State University ENSC 3233 Oklahoma State University

2. D-W Equation f = f (V, D, roughness & viscosity) ENSC 3233 Oklahoma State University

3. Friction Factor, f f e/D Re ENSC 3233 Oklahoma State University

4. Julius Weisbach, 1845 Source: H. Rouse, 1957 ENSC 3233 Oklahoma State University

5. Antoine Chézy, ~ 1770 Source: H. Rouse, 1957 ENSC 3233 Oklahoma State University

6. Poiseuille (1841) & Hagen (1839) Source: H. Rouse, 1957 ENSC 3233 Oklahoma State University

7. Osborne Reynolds, 1883 Laminar < 2,000 2,000 > Critical > 4,000 Turbulent > 4,000 Source:www.eng.man.ac.uk/historic/reynolds/orey1904.jpg laminar flow ENSC 3233 Oklahoma State University

8. Friction Factor, f f e/D Re ENSC 3233 Oklahoma State University

9. Henry Darcy, 1857 For cast iron at high flow For all conditions Source: G. Brown 2002 ENSC 3233 Oklahoma State University

10. John Fanning, 1877 Source: H. Rouse, 1976 ENSC 3233 Oklahoma State University

11. Ludwig Prandtl originator of boundary layer theory and advisor to von Kármán, Blasius, Nikuradse and others Source:www.ae.go.dlr.de/~send/Prandtl-Exhibition/wasserkanal.html ENSC 3233 Oklahoma State University

12. Paul Blasius, 1913 for smooth pipes (using data from Nikuradse) ENSC 3233 Oklahoma State University

13. Friction Factor, f f e/D Re ENSC 3233 Oklahoma State University

14. Theodor von Kármán, 1930 for rough pipes at high Re (based on data from Nikuradse) ENSC 3233 Oklahoma State University

15. Friction Factor, f f e/D Re ENSC 3233 Oklahoma State University

16. Johann Nikuradse, 1933 artificial sand roughness Source: W. Hager, 2004 ENSC 3233 Oklahoma State University

17. Cyril F. Colebrook, 1939 Source: W. Hager, 2004 Colebrook and White completed several papers on pipe friction in the 1930’s. The last under Colebrook’s name contained, for commercial pipe in transition zone ENSC 3233 Oklahoma State University

18. Friction Factor, f f e/D Re ENSC 3233 Oklahoma State University

19. Hunter Rouse, 1942 integration Re f Source: H. Rouse, 1976 ENSC 3233 Oklahoma State University

20. Lewis Moody, 1944 “convenient form” Source: H. Rouse, 1976 ENSC 3233 Oklahoma State University

21. A Rose by Any Other Name • The D-W equation has had a confusing history of nomenclature and usage. • Weisbach’s Eq. • Darcy’s Eq. • Chezy’s Eq. • Fanning’s Eq.(still used in Chemical Eng.) • No Name or Pipe Flow Eq. • Darcy-Weisbach – Popularized by Rouse • and adopted by ASCE in 1962. ENSC 3233 Oklahoma State University

22. Misnamed? The f vs Re diagram is almost universally credited to Moody, and the contributions of others are seldom acknowledged. This was a sore point for Hunter Rouse even though he had sincere respect for Moody. In 1976 Rouse wrote in the third person, ENSC 3233 Oklahoma State University

23. Misnamed? (cont) "After the conference, Lewis Moody of Princeton suggested using the latter variables (f and Re) as primary rather than supplementary, as in the past, but Rouse resisted the temptation because he felt that to do would be a step backward. So Moody himself published such a plot, and it is known around the world as the Moody diagram!" ENSC 3233 Oklahoma State University

24. Closing Comments • Little has changed in the D-W application since Moody’s 1944 publication. • The critical zone is still undefined. • Pipe roughness is difficult to estimate. • It is thus surprising that the f diagram has not been modified or replaced over the last 58 years. ENSC 3233 Oklahoma State University

25. A Warning from Henry Darcy In a letter to Henri Bazin, Darcy quoted François I who wrote, "Often women vary: he is quite mad who has faith in them", which Darcy amended with, "is no less true for hydraulic coefficients than for women." ENSC 3233 Oklahoma State University