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

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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D-W Equation
f f (V, D, roughness viscosity)
3
Friction Factor, f
f
e/D
Re
4
Julius Weisbach, 1845
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Antoine Chézy, 1770
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Poiseuille (1841) Hagen (1839)
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Osborne Reynolds, 1883
Laminar lt 2,000 2,000 gt Critical gt
4,000 Turbulent gt 4,000
laminar flow
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Friction Factor, f
f
e/D
Re
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Henry Darcy, 1857
For cast iron at high flow
For all conditions
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John Fanning, 1877
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Ludwig Prandtl
originator of boundary layer theory and advisor
to von Kármán, Blasius, Nikuradse and others
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Paul Blasius, 1913
for smooth pipes
(using data from Nikuradse)
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Friction Factor, f
f
e/D
Re
14
Theodor von Kármán, 1930
for rough pipes at high Re
(based on data from Nikuradse)
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Friction Factor, f
f
e/D
Re
16
Johann Nikuradse, 1933
artificial sand roughness
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C. F. Colebrook, 1939
Colebrook and White completed several papers on
pipe friction in the 1930s. The last under
Colebrooks name contained,
for commercial pipe in transition zone
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Friction Factor, f
f
e/D
Re
19
Hunter Rouse, 1942
integration
Re
f
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Lewis Moody, 1944
convenient form
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A Rose by Any Other Name

• The D-W equation has had a confusing history of
  nomenclature and usage.
• Weisbachs Eq.
• Darcys Eq.
• Chezys Eq.
• Fannings 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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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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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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Closing Comments

• Little has changed in the D-W application since
  Moodys 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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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."