Precise Explicit Approximations of the Colebrook-White Equation for Engineering Systems

Abstract

Modern automated engineering systems have variable hydraulic/aero- dynamic conditions with Reynolds number from zero to hundred thousand with a wide range of roughness. Simple approximations of the Colebrook-White equa- tion cannot give enough precision. The aim of the work is a universal simple precise approximation of the Colebrook-White equation. The methods are se- lected by the analysis of the equation curve. In the whole range of turbulent flow, it is near to linear. Thus, Newton’s method is very effective. The algorithm is proposed for getting high-precision approximations. The results are two simple explicit ones for rough and careful calculations with a deviation of 5.36 % and 0.00072 % in a wide range of parameters. It is shown on the examples of the objects: the highest building “Biotecton” and researches of “green roofs” in a wind tunnel. The scientific novelty is that we scientifically grounded the effective usage of Newton’s method, which provides new universal, precise and simple explicit approximations of Colebrook-White equation. The practical value is that the approximations are covered different practical tasks of hydraulic and aerody- namic calculations in the whole range of turbulent flow.