1. ENSC 3233 Oklahoma State University1 Everything you did (not) want to know about the Darcy- Weisbach Equation ENSC 3233 Oklahoma State University

2. ENSC 3233 Oklahoma State University2 D-W Equation f =  (V, D, roughness & viscosity)

3. ENSC 3233 Oklahoma State University3 f  /D Re Friction Factor, f

4. ENSC 3233 Oklahoma State University4 Julius Weisbach, 1845

5. ENSC 3233 Oklahoma State University5 Antoine Chézy, ~ 1770

6. ENSC 3233 Oklahoma State University6 Poiseuille (1841) & Hagen (1839)

7. ENSC 3233 Oklahoma State University7 Osborne Reynolds, 1883 laminar flow Laminar < 2,000 2,000 > Critical > 4,000 Turbulent > 4,000

8. ENSC 3233 Oklahoma State University8 f  /D Re Friction Factor, f

9. ENSC 3233 Oklahoma State University9 Henry Darcy, 1857 For cast iron at high flow For all conditions

10. ENSC 3233 Oklahoma State University10 John Fanning, 1877

11. ENSC 3233 Oklahoma State University11 Ludwig Prandtl originator of boundary layer theory and advisor to von Kármán, Blasius, Nikuradse and others

12. ENSC 3233 Oklahoma State University12 Paul Blasius, 1913 for smooth pipes (using data from Nikuradse)

13. ENSC 3233 Oklahoma State University13 f  /D Re Friction Factor, f

14. ENSC 3233 Oklahoma State University14 Theodor von Kármán, 1930 for rough pipes at high Re (based on data from Nikuradse)

15. ENSC 3233 Oklahoma State University15 f  /D Re Friction Factor, f

16. ENSC 3233 Oklahoma State University16 Johann Nikuradse, 1933 artificial sand roughness

17. ENSC 3233 Oklahoma State University17 Cyril F. Colebrook, 1939 for commercial pipe in transition zone Colebrook and White completed several papers on pipe friction in the 1930’s. The last under Colebrook’s name contained,

18. ENSC 3233 Oklahoma State University18 f  /D Re Friction Factor, f

19. ENSC 3233 Oklahoma State University19 Hunter Rouse, 1942 integration f Re

20. ENSC 3233 Oklahoma State University20 Lewis Moody, 1944 “convenient form”

21. ENSC 3233 Oklahoma State University21 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.

22. ENSC 3233 Oklahoma State University22 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,

23. ENSC 3233 Oklahoma State University23 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!"

24. ENSC 3233 Oklahoma State University24 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.

25. ENSC 3233 Oklahoma State University25 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."