Analysis of the Colebrook-White Equation and further approaches to solve Fluid Loss Coefficient Definition Problems

With the advancement of fluid mechanics in engineering, the need to estimate the pressure drop coefficient, becomes necessary for flow loss calculations in order to be able to measure pipe diameter or stipulate flow regimes that are required for a given situation. This coefficient appears in the Darcy-Weisbach formula in equality with the Poiseuille equation and is now measured by the Colebrook-White equation. However, because this equation presents a different characteristic, where the coefficient appears on both sides of the same equation, scholars of the area over time modeled approximations derived from this previous knowledge. In this work we will approach the Colebrook-White principles and their subsequent approaches. The aim of this paper is to analyze the correlations cited, as well as their authors, also analyzing the relative errors between the approximations and the Colebrook-White equation at specific intervals for the relative roughness and the Reynolds number and, from this, to determine which ones. have the lowest relative error.