Estimating drag coefficient for arrays of rigid cylinders representing emergent vegetation

Flow resistance due to vegetation is of interest for a wide variety of hydraulic engineering applications. This note evaluates several practical engineering functions for estimating bulk drag coefficient (C_D) for arrays of rigid cylinders, which are commonly used to represent emergent vegetation. Many of the evaluated functions are based on an Ergun-derived expression that relates C_D to two coefficients, describing viscous and inertial effects. A re-parametrization of the Ergun coefficients based on cylinder diameter (d) and solid volume fraction (φ) is presented. Estimates of C_D are compared to a range of experimental data from previous studies. All functions reasonably estimate C_D at low φ and high cylinder Reynolds numbers (R_d). At higher φ they typically underestimate C_D. Estimates of C_D utilizing the re-parametrization presented here match the experimental data better than estimates of C_D made using the other functions evaluated, particularly at low φ and low R_d.