Abstract

ALFARO-GUERRA, Marco; GUERRA-ROJAS, Rodrigo  and  OLIVARES-GALLARDO, Alan. Evaluation of the recursion depth of the analytical solution of the Colebrook-White equation in the accuracy of the friction factor prediction. Ing. invest. y tecnol. [online]. 2020, vol.21, n.4, 00008.  Epub Nov 20, 2020. ISSN 2594-0732.  https://doi.org/10.22201/fi.25940732e.2020.21.4.036.

The Colebrook equation, better known as the Colebrook-White equation, is valued for its accuracy in the prediction of the friction factor in cylindrical pipes in turbulent flow zone and is therefore widely used in the calculation of load losses. This equation is implicit and must be solved using numerical methods or by approximations such as the Lambert W function. In 2015, Mikata and Walczak proposed an exact analytical solution of the friction factor equation that presents a recursive structure, so the search for the exact solution of the Colebrook equation requires a lot of time and consumes significant computational resources. For this reason, this work shows the level of accuracy in the calculation of the friction factor, represented by the error obtained when implementing the analytical solution based on the depth of recursion “n”, for which a macro of Excel in VBA language. The originality of the present work corresponds to the evaluation of the accuracy in the prediction of the friction factor, in the range of practical use of the engineering equation considering relative roughness values of 10-1 to 10-6 and Reynolds numbers values from 104 to 108, which generates an analysis matrix that contains 839,937 data. As a result of the analysis performed, it can be concluded that the precision of the solution of the Colebrook equation depends on the depth of recursion, reaching a maximum relative error of 5,369E-08 % for a recursion depth of n=10.

Keywords : Friction factor; Colebrook equation; analytical solution; recursion depht.

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