A New Formula for Friction Factor-Reynolds Number of Non-Newtonian Fluids

Ouda, Ahmed A.; Hussein, Ehab S.; Shkarah, Ahmed Jassim; Mansour, Mustafa

doi:10.24271/psr.2025.516478.2081

A New Formula for Friction Factor-Reynolds Number of Non-Newtonian Fluids

Document Type : Original Article

Authors

Ahmed A. Ouda

Ehab S. Hussein

ahmed jassim shkarah

Mustafa Mansour

Department of Mechanical Engineering, College of Engineering, University of Thi-Qar, Thi-Qar, 64001, Iraq.

10.24271/psr.2025.516478.2081

Abstract

This study presents a new unified correlation to describe the relationship between the friction factor and Reynolds number for non-Newtonian fluids across laminar, transitional, and turbulent flow regimes. The proposed formula is developed using power-law-based curve fitting, integrating multiple regimes into a continuous function with coefficients dependent on the flow behavior index (n). Unlike existing models such as Metzner-Otto and Joseph-Yang, this approach improves prediction accuracy for a wide range of non-Newtonian fluids, including shear-thinning and shear-thickening types. The model was validated against experimental data, demonstrating a maximum relative error of 7.15% and improved accuracy particularly for low-index (n < 1) fluids. This correlation enables accurate flow regime classification and simplifies friction factor estimation without iterative methods, offering practical advantages in fluid transport system design.

Keywords

power law index

Flow regime classification

Generalized Reynolds number

rheology