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Colebrook–White Equation for Darcy–Weisbach Friction Factor

The Colebrook–White equation expresses the Darcy friction factor as a function of the Reynolds number and pipe relative roughness, fitting the data of experimental studies of turbulent flow in smooth and rough pipes.

The Colebrook-White equation relates the relative pipe roughness, Reynolds number and Darcy-Weisbach friction factor through a series of logarithms.

Formula

1/Sqrt[QuantityVariable["λ", "DarcyWeisbachFrictionFactor"]] == (-2*Log[0.27027027027027023*QuantityVariable["K", "Unitless"] + 2.51/(QuantityVariable["Re", "ReynoldsNumber"]*Sqrt[QuantityVariable["λ", "DarcyWeisbachFrictionFactor"]])])/Log[10]

symbol description physical quantity
λ Darcy­Weisbach friction factor "DarcyWeisbachFrictionFactor"
K relative pipe roughness "Unitless"
Re Reynolds number "ReynoldsNumber"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Colebrook\[Dash]White Equation for \ Darcy\[Dash]Weisbach Friction Factor"]
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Get the formula:

In[2]:=
FormulaData[ ResourceObject[ "Colebrook\[Dash]White Equation for Darcy\[Dash]Weisbach Friction \ Factor"]]
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Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Colebrook\[Dash]White Equation for Darcy\[Dash]Weisbach Friction \ Factor"], {QuantityVariable["Re","ReynoldsNumber"] -> 5000, QuantityVariable["\[Lambda]","DarcyWeisbachFrictionFactor"] -> 0.1`}]
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