Colebrook-White Equation

Colebrook-White equation, also called Colebrook equation or Colebrook formula, is a mathematical expression used in fluid dynamics and engineering to calculate the friction factor (also called Darcy friction factor) in a pipe or conduit for fluid flow.  It is primarily used in problems related to the flow of fluids in pipes, especially for turbulent flow conditions.

The Colebrook-White equation is an implicit equation, meaning that the friction factor $f$ appears on both sides of the equation.  Therefore, it is typically solved iteratively using numerical methods or software tools.  Engineers and fluid dynamicists use this equation to estimate the friction factor in order to analyze and design pipelines and ducts for fluid transport systems.

The Colebrook-White equation is particularly useful for turbulent flow, where the flow is characterized by chaotic and irregular fluid motion.  It provides a more accurate representation of the friction factor than simpler equations like the Darcy-Weisbach equation with a constant friction factor.

 

Colebrook-White Equation
\( 1\;/\; \sqrt{f} \;=\; - 2 \; log_{10} \; [\; ( \epsilon\ \;/\; 3.7 \; d_h ) + ( 2.51 \;/\; Re \; \sqrt{ f }\; ) \;] \)
Symbol	English	Metric
\( \epsilon \) (Greek symbol epsilon) = Absolute Roughness	\( in \)	\( mm \)
\( f \) = Friction Factor	\( dimensionless \)	\( dimensionless \)
\( d_h \) = Hydraulic Diameter	\( in \)	\( mm \)
\( Re \) = Reynolds Number	\( dimensionless \)	\( dimensionless \)