ENSC 3233 Oklahoma State University1 Everything you did (not) want to know about the Darcy- Weisbach...
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Transcript of ENSC 3233 Oklahoma State University1 Everything you did (not) want to know about the Darcy- Weisbach...
ENSC 3233 Oklahoma State University
1
Everything you did (not) want to know about the Darcy-Weisbach Equation
ENSC 3233Oklahoma State University
ENSC 3233 Oklahoma State University
2
D-W Equation
g
V
D
fLhl 2
2
f = (V, D, roughness & viscosity)
hl
D VL
ENSC 3233 Oklahoma State University
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Osborne Reynolds, 1883
VD
Re
Re
64f laminar
flow
Laminar < 2,0002,000 > Critical > 4,000
Turbulent > 4,000
ENSC 3233 Oklahoma State University
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Henry Darcy, 1857
2
2
'' V
DV
DD
Lhl
2"" V
DD
Lhl
For cast iron at high flow
For all conditions
ENSC 3233 Oklahoma State University
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Ludwig Prandtl
originator of boundary layer theory and advisor to von Kármán, Blasius, Nikuradse and others
ENSC 3233 Oklahoma State University
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Paul Blasius, 1913
4/1
3164.0
Ref
for smooth pipes
(using data from Nikuradse)
08.0log21
ff
Re
ENSC 3233 Oklahoma State University
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Theodor von Kármán, 1930
Df
log214.1
1
for rough pipes at high Re
(based on data from Nikuradse)
ENSC 3233 Oklahoma State University
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Cyril F. Colebrook, 1939
fDf Re
35.9log214.1
1 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,
ENSC 3233 Oklahoma State University
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A Rose by Any Other NameThe 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.
ENSC 3233 Oklahoma State University
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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,
ENSC 3233 Oklahoma State University
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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!"
ENSC 3233 Oklahoma State University
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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.