Explicit Friction Factor Correlation for Turbulent Flow in Smooth Pipes

Abstract

We present a truly explicit representation of the Nikuradse, Prandtl, von Kármán (NPK) friction factor equation for turbulent fluid flow in smooth pipes. Specifically, the Lambert W function is used to relate the friction factor explicitly to the Reynolds number. In addition to the elegance of an explicit expression, this new representation allows for the computation of friction factor values that are accurate to machine precision. As this is an exact explicit representation, it is far more accurate than current methods such as graphical estimation of friction factors from friction factor versus Reynolds number charts or several other explicit approximations of the NPK equation. We believe that this is the first truly explicit representation of the NPK equation and the elegance and high accuracy of this representation should make it the method of choice for estimating turbulent flow friction factors in smooth pipes.