Accurate and Efficient Explicit Approximations of the Colebrook Flow Friction Equation Based on the Wright ω-Function: Reply to the Discussion by Majid Niazkar

Abstract

In this reply, we present updated approximations to the Colebrook equation for flow friction. The equations are equally computational simple, but with increased accuracy thanks to the optimization procedure, which was proposed by the discusser, Dr. Majid Niazkar. Our large-scale quasi-Monte Carlo verifications confirm that the here presented novel optimized numerical parameters further significantly increase accuracy of the estimated flow friction factor.

Keywords

• Colebrook equation
• hydraulic resistance
• Lambert W-function
• Wright ω-function
• explicit approximations
• computational burden