Based on mechanical derivation, a new formula showing the effects of emergent vegetation on Manning’s coefficient was established for complex gradually varied flow affected by rigid unsubmerged vegetation in open channels. The new formula indicates that the Manning’s coefficient is a quadratic sum of its vegetal and boundary components with coefficients related to vegetation parameters. The variation characteristics of the total Manning’s coefficient and its vegetal component calculated by the new formula were investigated by a series of laboratory experiments under different vegetation coverage area ratios. It was found that the variations of both the total Manning’s coefficient and its vegetal component followed a linear decreasing trend along the vegetation section. Moreover, linear and power empirical formulas were constructed for the average total Manning’s coefficient and its vegetal component related to the vegetation coverage area ratio, respectively. The findings of the research may expand the theoretical connotations of the Manning’s coefficient for open channel hydraulics and demonstrate practical significance to engineering applications of the Manning’s coefficient for gradually varied flow in vegetated channels.

Introduction

Manning’s coefficient, which was proposed by the Irish engineer Robert Manning, comprehensively reflects the influence of channel roughness on water flow, and is widely used in traditional hydraulics to determine the degree of roughness in natural open channels [1], [2]. With decades of research in the field, Chow evaluated and tabulated the values of Manning’s coefficient for different surface roughness values [3]. However, the hydraulic conditions, such as flow resistance, are significantly changed as vegetation blocks the water flow into a partially continuous system [4], [5]. Numerous papers can be found in the literature that focus on the evaluation of vegetation effects on channel roughness [6]–[۹]. For vegetated channel flow, Palmer proposed an empirical relationship in which the Manning’s coefficient is related to the product of the flow velocity v and the hydraulic radius R [10], [11]. Engineers have adapted this relationship in the design of irrigation channels and other vegetated waterways [3]. Nonetheless, experimental studies by Kouwen and Li indicated that the Manning’s coefficient is not always linearly related to the product of flow velocity and hydraulic radius [12].