1. The History of the Darcy-Weisbach Equation for Pipe Flow Resistance
Glenn O. Brown
Oklahoma State University
2002, ASCE National, Washington D.C.
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2. D-W Equation f = f (V, D, roughness & viscosity)
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3. Friction Factor, f f
e/D Re
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4. Julius Weisbach, 1845
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5. Antoine Chézy, ~ 1770
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6. Poiseuille (1841) & Hagen (1839)
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7. Osborne Reynolds, 1883 Laminar < 2,000
2,000 > Critical > 4,000
Turbulent > 4,000
laminar flow
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8. Friction Factor, f f
e/D Re
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9. Henry Darcy, 1857 For cast iron at high flow For all conditions
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10. John Fanning, 1877
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11. Ludwig Prandtl
originator of boundary layer theory and advisor to von Kármán, Blasius, Nikuradse and others
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12. Paul Blasius, 1913 for smooth pipes (using data from Nikuradse)
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13. Friction Factor, f f
e/D Re
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14. Theodor von Kármán, 1930 for rough pipes at high Re
(based on data from Nikuradse)
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15. Friction Factor, f f
e/D Re
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16. Johann Nikuradse, 1933 artificial sand roughness
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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
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18. Friction Factor, f f
e/D Re
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19. Hunter Rouse, 1942
integration Re f
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20. Lewis Moody, 1944
“convenient form”
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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.
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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,
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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!"
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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.
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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."
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