Unified Friction Formulation from Laminar to Fully Rough Turbulent Flow

TL;DR

This paper introduces a new unified formula for Newtonian fluid flow in pipes that seamlessly covers all regimes from laminar to fully rough turbulent, improving transition modeling and computational efficiency.

Contribution

A novel unified formula that accurately models all pipe flow regimes using switching functions, enhancing transition smoothness and computational simplicity.

Findings

The formula captures all flow regimes from laminar to fully rough turbulent.

It provides smooth, computationally efficient transitions among flow regimes.

Comparison shows improved modeling over existing literature.

Abstract

This paper gives a new unified formula for the Newtonian fluids valid for all pipe flow regimes from laminar to the fully rough turbulent. It includes laminar, unstable sharp jump from laminar to turbulent, and all types of the turbulent regimes: smooth turbulent regime, partial non-fully developed turbulent and fully developed rough turbulent regime. The formula follows the inflectional form of curves as suggested in Nikuradse's experiment rather than monotonic shape proposed by Colebrook and White. The composition of the proposed unified formula consists of switching functions and of the interchangeable formulas for laminar, smooth turbulent and fully rough turbulent flow. The proposed switching functions provide a smooth and a computationally cheap transition among hydraulic regimes. Thus, the here presented formulation represents a coherent hydraulic model suitable for engineering use. The model is compared to existing literature models, and shows smooth and computationally cheap transitions among hydraulic regimes.