This paper focuses on the dissipative similarity of step-pool units at rill, flume and stream scale. This investigation is carried out using recent advances in open channel flow resistance, applications of close-range photogrammetry to rill erosion, available published data on step-pool features in flumes and streams and a new dataset of measurements in fixed bed step-pool rills. A theoretically-based equation for calculating the Darcy-Weisbach friction factor obtained by integration of a power velocity profile is presented. The scale factor Γ of this power velocity profile, which is included in the flow resistance equation, was previously calibrated (Eq. 10) for mobile bed rills with step-pool units. At first, in this investigation an additional test of this flow resistance equation is developed using measurements carried out in fixed bed rills with step-pool features. In particular, the proposed Γ function is tested using the measurements carried out in 63 fixed bed rill reaches incised on a 24 and 26% sloped plot. This test shows that the effect of sediment transport on the flow resistance law can be considered negligible as compared to the effect of the form-induced dissipative mechanisms due to the presence of step-pools structures. Then, using measurements carried out in 61 flume experimental runs and 109 reaches of step-pool streams, this investigation demonstrates that the Γ function for flume and stream conditions can be obtained scaling that (Eq. 10) determined for step-pool rills. The Darcy-Weisbach friction factor values measured in flumes and streams are, on average, higher than those related to rills. Finally, the application of the theoretical equation for calculating the Darcy-Weisbach friction factor for flume and stream conditions requires Γ, estimated by Eq. (10), to be multiplied by a specific scale factor.

本文关注阶梯池单元在小溪，水槽和水流尺度下的耗散相似性。这项研究是利用明渠流动阻力的最新进展，近距离摄影测量法对小溪侵蚀的应用，在河道和河流中阶梯池特征的可用公开数据以及固定床阶梯池小溪的新测量数据集进行的。提出了一种基于理论的方程，用于计算通过积分功率速度曲线获得的达西-魏斯巴赫摩擦因数。包含在流阻方程中的该功率速度曲线的比例因子Γ事先已针对带有阶梯式泳池装置的移动式床钻进行了校准（公式10）。首先，在这项研究中，使用在带有阶梯池特征的固定床钻具中进行的测量，开发了对该流阻方程的附加测试。特别是，建议的Γ函数是使用在24％和26％的坡度图上切开的63个固定床小河段中进行的测量来测试的。该试验表明，与台阶引起的耗散机制的影响相比，泥沙运移对流动阻力规律的影响可以忽略不计。然后，使用在61个水槽实验运行中进行的测量和109步阶梯式水流的测量，该研究表明，对于水槽和水流条件的Γ函数可以按比例（对于方程式10）确定的比例获得（公式10）。平均而言，在水槽和河流中测得的达西-魏斯巴赫摩擦系数值高于与小溪有关的值。最后，理论公式在计算水槽和水流条件下的达西-魏斯巴赫摩擦因数时需要使用由等式估算的Γ。（10）乘以特定比例因子。