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The History of the Darcy-Weisbach Equation for Pipe Flow Resistance

The History of the Darcy-Weisbach Equation for Pipe Flow Resistance. Glenn O. Brown Oklahoma State University 2002, ASCE National, Washington D.C. D-W Equation. f = f ( V, D, roughness & viscosity). Friction Factor, f. f. e /D. Re. Julius Weisbach, 1845. Antoine Chézy, ~ 1770.

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The History of the Darcy-Weisbach Equation for Pipe Flow Resistance

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  1. The History of the Darcy-Weisbach Equation for Pipe Flow Resistance Glenn O. Brown Oklahoma State University 2002, ASCE National, Washington D.C. ASCE 150th Anniversary

  2. D-W Equation f = f (V, D, roughness & viscosity) ASCE 150th Anniversary

  3. Friction Factor, f f e/D Re ASCE 150th Anniversary

  4. Julius Weisbach, 1845 ASCE 150th Anniversary

  5. Antoine Chézy, ~ 1770 ASCE 150th Anniversary

  6. Poiseuille (1841) & Hagen (1839) ASCE 150th Anniversary

  7. Osborne Reynolds, 1883 Laminar < 2,000 2,000 > Critical > 4,000 Turbulent > 4,000 laminar flow ASCE 150th Anniversary

  8. Friction Factor, f f e/D Re ASCE 150th Anniversary

  9. Henry Darcy, 1857 For cast iron at high flow For all conditions ASCE 150th Anniversary

  10. John Fanning, 1877 ASCE 150th Anniversary

  11. Ludwig Prandtl originator of boundary layer theory and advisor to von Kármán, Blasius, Nikuradse and others ASCE 150th Anniversary

  12. Paul Blasius, 1913 for smooth pipes (using data from Nikuradse) ASCE 150th Anniversary

  13. Friction Factor, f f e/D Re ASCE 150th Anniversary

  14. Theodor von Kármán, 1930 for rough pipes at high Re (based on data from Nikuradse) ASCE 150th Anniversary

  15. Friction Factor, f f e/D Re ASCE 150th Anniversary

  16. Johann Nikuradse, 1933 artificial sand roughness ASCE 150th Anniversary

  17. C. F. Colebrook, 1939 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 ASCE 150th Anniversary

  18. Friction Factor, f f e/D Re ASCE 150th Anniversary

  19. Hunter Rouse, 1942 integration Re f ASCE 150th Anniversary

  20. Lewis Moody, 1944 “convenient form” ASCE 150th Anniversary

  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. ASCE 150th Anniversary

  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, ASCE 150th Anniversary

  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!" ASCE 150th Anniversary

  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. ASCE 150th Anniversary

  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." ASCE 150th Anniversary

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