Colebrook–White equation

The unknown friction factor f appears on the left and inside the square-root term on the right, so algebra does not isolate it directly. Start with a guess, recompute the right-hand side and iterate until the value changes little. Explicit approximations are available but should be identified as approximations. Colebrook gives the Darcy factor for its stated pipe-flow regime. Report Reynolds number, relative roughness and factor convention together. Application: Estimate turbulent friction losses in technical pipes. The numerical example At Re=100,000 and ε/D=0.001, iteration gives Darcy f≈0.0222. Substitution gives a right side near 6.71, matching 1/√0.0222≈6.71. Head loss then uses Darcy–Weisbach; do not substitute the Fanning factor anchors the idea in a concrete measurement case.

Both factors describe pipe friction but use different definitions. Darcy–Weisbach f is four times the Fanning factor. The displayed Colebrook equation returns Darcy f; inserting it into a Fanning-form equation mis-scales pressure loss. State the convention in both calculations and references. Colebrook gives the Darcy factor for its stated pipe-flow regime. Report Reynolds number, relative roughness and factor convention together. The corresponding units are Darcy f dimensionless; ε and D in m; Re dimensionless. At Re=100,000 and ε/D=0.001, iteration gives Darcy f≈0.0222. Substitution gives a right side near 6.71, matching 1/√0.0222≈6.71. Head loss then uses Darcy–Weisbach; do not substitute the Fanning factor. This checks that the reference quantities are compatible.

It models fully developed turbulent flow in engineering pipes. Laminar round-pipe flow has f=64/Re; transition is sensitive and not reliably covered by this correlation. Entrance regions, noncircular ducts and strongly unsteady flow need other models or corrections. Check the regime before iterating. Colebrook gives the Darcy factor for its stated pipe-flow regime. Report Reynolds number, relative roughness and factor convention together. Scope: This correlation applies approximately to fully developed turbulent engineering pipe flow and combines viscous and roughness effects. It is implicit in f, so solve iteratively or use a stated approximation. Use Darcy f, not the Fanning factor, smaller by four. Laminar round-pipe flow uses f=64/Re; transition is not reliably described by Colebrook. A practical application is Estimate turbulent friction losses in technical pipes.

The Darcy friction factor appears on both sides, including inside the logarithm. It therefore cannot generally be isolated by elementary rearrangement; use iteration or a named approximation. Start with a plausible positive value and check the residual after updating. The solution also depends on Reynolds number and relative roughness; dimensionless inputs help compare pipes. Colebrook gives the Darcy factor for its stated pipe-flow regime. Report Reynolds number, relative roughness and factor convention together. Check the calculation with this case: At Re=100,000 and ε/D=0.001, iteration gives Darcy f≈0.0222. Substitution gives a right side near 6.71, matching 1/√0.0222≈6.71. Head loss then uses Darcy–Weisbach; do not substitute the Fanning factor. Keep the model limits and units in view.

Colebrook gives the Darcy–Weisbach factor. Under matching conventions, the Fanning factor is four times smaller. Using the wrong factor in Darcy–Weisbach underestimates friction loss by four. Check the label and the pressure-loss equation in the source. Fully developed laminar circular-pipe flow uses fD=64/Re; the transition region has no equally reliable single formula. Colebrook gives the Darcy factor for its stated pipe-flow regime. Report Reynolds number, relative roughness and factor convention together. The relation describes The implicit Colebrook relation gives the Darcy friction factor for turbulent round-pipe flow from Reynolds number and relative roughness. This helps distinguish its target quantity from neighbouring quantities.