Explicit representation of the implicit Colebrook–White equation

• An analytical solution of the Colebrook–White equation is provided.
• The friction factor can be calculated with arbitrary accuracy.
• The whole (ϵ/D)-Re-space(ϵ/D)-Re-space can be calculated.
• Examples for practical applications are given.

It is shown that the Colebrook–White equation 1/λ=−2lg[2.51/Reλ+ϵ/3.71D] can be solved analytically for the friction factor λ  . The solution contains two infinite sums. For given Reynolds numbers ReRe and relative roughnesses ϵ/Dϵ/D, one can create an own approximation with the required accuracy by adding a finite number of summands. The computing time of both the iterative calculation and several approximations is being compared. In all cases, the approximation is much faster than the iteration. Two examples for practical applications are given.