Estimating drag coefficient for arrays of rigid cylinders representing emergent vegetation

Abstract

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