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ASCE 150th Anniversary1 The History of the Darcy- Weisbach Equation for Pipe Flow Resistance Glenn O. Brown Oklahoma State University 2002, ASCE National,

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Presentation on theme: "ASCE 150th Anniversary1 The History of the Darcy- Weisbach Equation for Pipe Flow Resistance Glenn O. Brown Oklahoma State University 2002, ASCE National,"— Presentation transcript:

1 ASCE 150th Anniversary1 The History of the Darcy- Weisbach Equation for Pipe Flow Resistance Glenn O. Brown Oklahoma State University 2002, ASCE National, Washington D.C.

2 ASCE 150th Anniversary2 D-W Equation f =  (V, D, roughness & viscosity)

3 ASCE 150th Anniversary3 f  /D Re Friction Factor, f

4 ASCE 150th Anniversary4 Julius Weisbach, 1845

5 ASCE 150th Anniversary5 Antoine Chézy, ~ 1770

6 ASCE 150th Anniversary6 Poiseuille (1841) & Hagen (1839)

7 ASCE 150th Anniversary7 Osborne Reynolds, 1883 laminar flow Laminar < 2,000 2,000 > Critical > 4,000 Turbulent > 4,000

8 ASCE 150th Anniversary8 f  /D Re Friction Factor, f

9 ASCE 150th Anniversary9 Henry Darcy, 1857 For cast iron at high flow For all conditions

10 ASCE 150th Anniversary10 John Fanning, 1877

11 ASCE 150th Anniversary11 Ludwig Prandtl originator of boundary layer theory and advisor to von Kármán, Blasius, Nikuradse and others

12 ASCE 150th Anniversary12 Paul Blasius, 1913 for smooth pipes (using data from Nikuradse)

13 ASCE 150th Anniversary13 f  /D Re Friction Factor, f

14 ASCE 150th Anniversary14 Theodor von Kármán, 1930 for rough pipes at high Re (based on data from Nikuradse)

15 ASCE 150th Anniversary15 f  /D Re Friction Factor, f

16 ASCE 150th Anniversary16 Johann Nikuradse, 1933 artificial sand roughness

17 ASCE 150th Anniversary17 C. 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 ASCE 150th Anniversary18 f  /D Re Friction Factor, f

19 ASCE 150th Anniversary19 Hunter Rouse, 1942 integration f Re

20 ASCE 150th Anniversary20 Lewis Moody, 1944 “convenient form”

21 ASCE 150th Anniversary21 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 ASCE 150th Anniversary22 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 ASCE 150th Anniversary23 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 ASCE 150th Anniversary24 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 ASCE 150th Anniversary25 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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