Abstract

ALFARO-GUERRA, Marco; GUERRA-ROJAS, Rodrigo  and  OLIVARES-GALLARDO, Alan. Experimental evaluation of exact analytical solution of the Colebrook-White Equation. Ing. invest. y tecnol. [online]. 2019, vol.20, n.2. ISSN 2594-0732.  https://doi.org/10.22201/fi.25940732e.2019.20n2.021.

In the present work a hydraulic system was designed and built for the experimental determination of the friction factor in a PVC pipe under turbulent flow. This system allows the water to be conducted through a pipeline where the flow and the pressure difference were measured to calculate the pressure loss between two control points, considering the properties associated with the pipe such as the relative roughness, diameter and length. Using the Darcy-Weisbach equation, the experimental friction factor was determined. The objective of the present work was to experimentally evaluate the friction factor and compare it with that obtained using the nth formula as an approximation of the exact solution of the Colebrook-White equation proposed by Mikata and Walczak in 2015. The nth formula, this predicts the friction factor with a relative error that tends to decrease depending on the depth of the recursion. In our analysis, for a value of n equal to 15, the error in the determination of the friction factor reported values lower than 1E-16. An Excel macro was developed in VBA language to evaluate the recursion given the numerical difficulty of solving the exact analytical value of the Colebrook-White equation. The originality of this work corresponds to the evaluation of the nth formula of the friction factor and its comparison with the experimental results obtained in the laboratory, which allows to prove the validity of the prediction of the formula with a real case. This allowed finding the percentage relative error with respect to the experimental value.

Keywords : Friction factor; analytical solution of the Colebrook-White Equation; pressure drop in pipes; infinite recursion; experimental system.

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