on the unsteady friction for transient flow mechanics: a comprehensive review of models, applications and challenges

A wide range of applied fluid mechanics problems are related to transient flows. in conventional analyses, the relationship between wall shear stress and average cross-sectional velocity — valid for steady flow — is often assumed to hold under unsteady conditions. this simplification, typically implemented through the darcy–weisbach or hazen–williams formulations, leads to an underestimation of frictional losses in rapid transients by up to 15–25% according to experimental studies. unsteady friction formulations incorporate an additional term to account for acceleration effects, thereby improving prediction accuracy. for instance, zielke's convolution-based model achieves less than 2% error in laminar regimes, while simplified approaches such as trikha's approximation reduce computational demand by approximately 60% with only a minor accuracy loss (<5%) for low-reynolds turbulent flows. instantaneous acceleration-based (iab) models, such as brunone's, can reduce pressure attenuation discrepancies by 10–18% compared to quasi-steady models, and two-coefficient iab variants further improve waveform agreement by separating temporal and spatial acceleration contributions. this review critically examines the major classes of unsteady friction models outlining their theoretical basis, computational performance, and applicability domains. furthermore, classification schemes, practical implementation aspects, challenges, and future research directions, including hybrid physics–machine learning approaches, are discussed in detail.