Redigerer Ligninger for Darcy-Weisbachs friksjonsfaktor (avsnitt)

==Tabell for approksimasjoner==
Tabellen under lister opp historiske approksimasjoner:<ref name=Beograd>{{cite journal|last=Beograd|first=Dejan Brkić|title=Determining Friction Factors in Turbulent Pipe Flow|journal=Chemical Engineering|date=mars 2012|pages=34–39|url=http://www.che.com/processing_and_handling/liquid_gas_and_air_handling/9059.html|url-tilgang=abonnement}}</ref> 

* Re er Reynoldstall (dimensjonsløst tall)
* f  er Darcy-Weisbach friksjonsfaktor (dimensjonsløs)
* &epsilon; er ruheten av rørets flater (spesifikt)
* ''D'' er indre rør diameter;
* <math>\log(x)</math> logaritmen med 10 som grunntall.

Merk at Churchill-ligningen<ref>{{cite journal | first=S.W. | last=Churchill | title=Friction-factor  equation spans all fluid-flow regimes | journal=Chemical Engineering | pages = 91–92 |date=7. november 1977}}</ref> (1977) er den eneste som gir en korrekt verdi for friksjonsfaktoren i det laminære strømningsområde (Reynolds tall < 2300). Alle de andre er bare for overgangs- og turbulent strømning. 

{| class="wikitable sortable" border="1"
|+ Table of Colebrook equation approximations
|-
! scope="col" class="unsortable"| Equation
! scope="col" | Author
! scope="col" | Year
|-
|
<math>
f = 0,0055 (1 + (2 \times10^4 \cdot\frac{\varepsilon}{D} + \frac{10^6}{Re} )^\frac{1}{3})
</math>
|Moody
|1947
|-
|
<math>
f = 0,094 (\frac{\varepsilon}{D})^{0,225} + 0,53 (\frac{\varepsilon}{D}) + 88 (\frac{\varepsilon}{D})^{0,44} \cdot {Re}^{-{\Psi}}
</math>
:hvor
:<math>\Psi = 1,62(\frac{\varepsilon}{D})^{0,134}</math>
|Wood
|1966
|-
|
<math>
\frac{1}{\sqrt{f}} = -2 \log (\frac{\varepsilon}{3,715D} + \frac{15}{Re})
</math>
|Eck
|1973
|-
|
<math>
\frac{1}{\sqrt{f}} = -2 \log (\frac{\varepsilon}{3,7D} + \frac{5,74}{Re^{0,9}})
</math>
|Jain and Swamee
|1976
|-
|
<math>
\frac{1}{\sqrt{f}} = -2 \log ((\frac{\varepsilon}{3,71D}) + (\frac{7}{Re})^{0,9})
</math>
|Churchill
|1973
|-
|
<math>
\frac{1}{\sqrt{f}} = -2 \log ((\frac{\varepsilon}{3,715D}) + (\frac{6,943}{Re})^{0,9}))
</math>
|Jain
|1976
|-
|
<math>
f = 8[(\frac{8}{Re})^{12} + \frac{1}{(\Theta_1 + \Theta_2)^{1,5}})]^{\frac{1}{12}}
</math>
:where
:<math>\Theta_1=[-2,457 \ln[(\frac{7}{Re})^{0,9} + 0,27\frac{\varepsilon}{D}]]^{16}</math>
:<math>\Theta_2 = (\frac{37530}{Re})^{16}</math>
|Churchill
|1977
|-
|
<math>
\frac{1}{\sqrt{f}} = -2 \log [\frac{\varepsilon}{3,7065D} - \frac{5,0452}{Re} \log(\frac{1}{2,8257}(\frac{\varepsilon}{D})^{1,1098} + \frac{5,8506}{Re^{0,8981}})]
</math>
|Chen
|1979
|-
|
<math>
\frac{1}{\sqrt{f}} = 1,8\log[\frac{Re}{0,135Re(\frac{\varepsilon}{D}) +6,5}]
</math>
|Round
|1980
|-
|
<math>
\frac{1}{\sqrt{f}} = -2 \log \left(\frac{\varepsilon}{3,7D} + \frac{5,158log(\frac{Re}{7})} {Re \left(1 + \frac{Re^{0,52}}{29} (\frac{\varepsilon}{D})^{0,7} \right)} \right)
</math>
|Barr
|1981
|-
|
<math>
\frac{1}{\sqrt{f}} = -2 \log [\frac{\varepsilon}{3,7D} - \frac{5,02}{Re} \log(\frac{\varepsilon}{3,7D} - \frac{5,02}{Re} \log(\frac{\varepsilon}{3,7D} + \frac{13}{Re}))]
</math>
:or
<math>
\frac{1}{\sqrt{f}} = -2 \log [\frac{\varepsilon}{3,7D} - \frac{5,02}{Re} \log(\frac{\varepsilon}{3,7D} + \frac{13}{Re})]
</math>
|Zigrang and Sylvester
|1982
|-
|
<math>
\frac{1}{\sqrt{f}} = -1,8 \log \left[\left(\frac{\varepsilon}{3,7D}\right)^{1,11} + \frac{6,9}{Re}\right]
</math>
|Haaland{{efn| Haalandligningen ble foreslått av professor Haaland ved Norges tekniske høgskole i 1984. Den brukes til å løse direkte ut for Darcy-Weisbach friksjonsfaktor ''f'' for en fylt sirkulært rør. Det er en tilnærming til den implisitte Colebrook-White ligningen, men avviket fra eksperimentelle data er godt innenfor nøyaktigheten av dataene. Den ble utviklet av S. E. Haaland i 1983 .}}<ref name="ReferenceA"/>
|1983
|-
|
<math>
f = [\Psi_1 - \frac{(\Psi_2-\Psi_1)^{2}}{\Psi_3-2\Psi_2+\Psi_1}]^{-2}</math>
:or
<math>
f = [4,781 - \frac{(\Psi_1-4,781)^{2}}{\Psi_2-2\Psi_1+4,781}]^{-2}</math>
:where
:<math>\Psi_1 = -2\log(\frac{\varepsilon}{3,7D} + \frac{12}{Re})</math>
:<math>\Psi_2 = -2\log(\frac{\varepsilon}{3,7D} + \frac{2,51\Psi_1}{Re})</math>
:<math>\Psi_3 = -2\log(\frac{\varepsilon}{3,7D} + \frac{2,51\Psi_2}{Re})</math>
|Serghides
|1984
|-
|
<math>
\frac{1}{\sqrt{f}} = -2 \log(\frac{\varepsilon}{3,7D} + \frac{95}{Re^{0,983}} - \frac{96,82}{Re})</math>
|Manadilli
|1997
|-
|
<math>
\frac{1}{\sqrt{f}} = -2 \log \lbrace \frac{\varepsilon}{3,7065D}-\frac{5,0272}{Re}\log[\frac{\varepsilon}{3,827D}- \frac{4,657}{Re} \log ((\frac{\varepsilon}{7,7918D})^{0,9924} + (\frac{5,3326}{208,815 + Re})^{0,9345})] \rbrace </math>
|Monzon, Romeo, Royo
|2002
|-
|
<math>
\frac{1}{\sqrt{f}} = 0,8686 \ln[\frac{0,4587Re}{(S-0,31)^{\frac{S}{(S+1)}}}]
</math>
:hvor:
:<math>S = 0,124Re \frac{\varepsilon}{D} + \ln (0,4587Re)</math>
|Goudar, Sonnad
|2006
|-
|
<math>
\frac{1}{\sqrt{f}} = 0,8686 \ln[\frac{0,4587Re}{(S-0,31)^{\frac{S}{(S+0,9633)}}}]
</math>
:hvor:
:<math>S = 0,124Re \frac{\varepsilon}{D} + \ln (0,4587Re)</math>
|Vatankhah, Kouchakzadeh
|2008
|-
|
<math>
\frac{1}{\sqrt{f}} = \alpha - [ \frac {\alpha + 2\log(\frac{\Beta}{Re})}{1 + \frac{2.18}{\Beta}}]
</math>
:where
:<math>\alpha = \frac{(0,744\ln(Re)) - 1,41}{(1+ 1,32\sqrt{\frac{\varepsilon}{D}})}</math>
:<math>\Beta = \frac{\varepsilon}{3,7D}Re + 2,51\alpha</math>
|Buzzelli
|2008
|-
|
<math>
f = \frac{6,4}{(\ln(Re) -\ln(1+0,01Re\frac{\varepsilon}{D}(1+10\sqrt{\frac{\varepsilon}{D}})))^{2,4}}
</math>
|Avci, Kargoz
|2009
|-
|
<math>
\lambda = \frac{0,2479 - 0,0000947(7-\log Re)^{4}}{(\log(\frac{\varepsilon}{3,615D} + \frac{7,366}{Re^{0,9142}}))^{2}}
</math>
|Evangleids, Papaevangelou, Tzimopoulos
|2010
|}

{{løpenummer|lower-alpha}}
<references group="lower-alpha"/>