Optimization of the Colebrook-White Equation based on experimental data

Document Type : Article

Authors

D‌e‌p‌t. o‌f A‌e‌r‌o‌s‌p‌a‌c‌e E‌n‌g‌i‌n‌e‌e‌r‌i‌n‌g S‌h‌a‌h‌i‌d S‌a‌t‌t‌a‌r‌i A‌i‌r U‌n‌i‌v‌e‌r‌s‌i‌t‌y

Abstract

Friction plays an important role in velocity distribution, shear stress, boundary layer, energy loss, and erosion. In the pressure drop, the friction factor has a direct relation with the Reynolds Number in smooth, turbulent, and transitional flows from the transition to the turbulence. Today, among engineers and researchers in fluid science, due to its wide applications, accurate calculation of the relations governing the friction factor is of high significance. Many attempts were made to improve the most famous friction factor equation, named Colebrook Equation, in the last century and since the , the experimental data have not been fully enriched with experimental data in various Reynolds regions. The purpose of the present study was to improve the Colebrook implicit equation, provide a more accurate equation in the wider Reynolds Region, and adapt it to valid experimental and laboratory data. Therefore, the current researcher tried to perform the calculations with the least changes to the equation of Colebrook explicit and with the greatest accuracy using the experimental data. The method used in this research utilizes graph engineering software, and the first-generation solution method such as one of the three conventional methods matches the approximations and adjusts the curves to the obtained data. The number of errors in different equations in all Reynolds regions, specifically, the last equations presented, was investigated and researched as the last accurate and practical equations presented. Then, with the obtained information, the present research equation was corrected and matched with experimental data. Finally, in order to prove the accuracy of the equation of the present study, the accuracy was compared with other equations and diagrams were drawn in all common Reynolds regions. The results indicate the advantage of using this research and its equation accuracy in specific Reynolds regions compared to other equations. Accuracy and adaptation are much higher than previous values in the widely used areas.

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References

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