Abstract This paper presents a direct closed form analytical solution for the implicit type equation of Colebrook-White for friction factor calculation. Based on the developed expression, the friction factor can be directly calculated given the fluid flow parameters namely the relative roughness and the Reynolds number. Obtained expression is explicit and it does not require any iterative calculation as it is built reposing on the analytical solution of a cubic equation of real coefficients. The used cubic equation is obtained through a 3rd order Taylor series expansion of the original Colebrook-White equation around an expansion point reasonably defined. The reliability of the proposed expression is proved through comparison with original Moody chart values as well as others results issued from previous approximations found in literature and the exact solution of Colebrook-White equation. The accuracy and the robustness of the established expression over other explicit correlations were emphasized. The presented closed form expression was proved to be simple, robust and accurate. Additionally it has the advantages of covering all the range of applicability of the original Colebrook-White equation.

中文翻译：

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Colebrook-White 方程的精确显式解析解

摘要 本文提出了用于摩擦系数计算的Colebrook-White隐式方程的直接闭合形式解析解。基于所开发的表达式，摩擦系数可以直接计算给定流体流动参数，即相对粗糙度和雷诺数。得到的表达式是明确的，不需要任何迭代计算，因为它是建立在实系数三次方程的解析解上的。使用的三次方程是通过原始 Colebrook-White 方程围绕合理定义的扩展点的三阶泰勒级数展开获得的。通过与原始穆迪图值以及从文献中发现的先前近似值和 Colebrook-White 方程的精确解得出的其他结果进行比较，证明了所提出的表达式的可靠性。强调了已建立的表达式相对于其他显式相关性的准确性和稳健性。所提出的闭式表达式被证明是简单、健壮和准确的。此外，它具有覆盖原始 Colebrook-White 方程所有适用范围的优点。