Abstract This study presents a generalized, theoretically grounded semi‐empirical framework for estimating flow resistance through canopies and granular beds, both of which are common in engineering and environmental applications. Derived from fundamental fluid mechanics principles, the proposed formulation significantly reduces reliance on empirical calibration parameters, enhancing both physical interpretability and applicability across diverse flow conditions. The model employs the hydraulic radius and average pore velocity as characteristic scales to relate drag coefficients and pressure drops. Utilizing the hydraulic radius as the characteristic length provides a unified geometric description applicable to any arbitrary shape. In contrast, existing formulas are typically limited to idealized geometries, such as cylinders and spheres. Validation against extensive experimental and numerical data sets demonstrates superior accuracy compared to conventional empirical formulas. Specifically, the framework yields a normalized root mean square error of 0.207 for flow through rigid cylinders and a root mean square logarithmic error of 0.0344 for flow through granular bed, performing consistently across varying solid volume fractions and Reynolds numbers. While minor discrepancies at high Reynolds numbers suggest potential areas for further improvement, the simplicity and universal applicability of this framework position it as a valuable tool for practical applications involving vegetation management, sediment transport modeling, and flow through porous media.
Tsai et al. (Wed,) studied this question.