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 (CD) 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 CD 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 CD are compared to a range of experimental data from previous studies. All functions reasonably estimate CD at low φ and high cylinder Reynolds numbers (Rd). At higher φ they typically underestimate CD. Estimates of CD utilizing the re-parametrization presented here match the experimental data better than estimates of CD made using the other functions evaluated, particularly at low φ and low Rd.