Assessing flow resistance in gravel bed channels by dimensional analysis and self-similarity

In this paper a new flow resistance equation for open channel flow, based on the integration of a power velocity profile, was tested for gravel bed channels. First this flow resistance equation, theoretically deduced by dimensional analysis and incomplete self-similarity condition, was reported. Then a relationship between the Gamma function of the velocity profile, the channel slope and the Froude number was calibrated by the available laboratory measurements of flow velocity, water depth and bed slope carried out in 416 flume experimental runs with a gravel bed. Then the relationship for estimating Gamma function and the theoretical resistance equation was tested by 83 independent flume measurements. The analysis also showed that the proposed flow resistance equation allows an estimate of the Darcy-Weisbach friction factor which is more reliable and accurate than that obtained by a semi-logarithmic flow resistance law or a variable-power resistance equation, calibrated with the same gravel bed measurements. For testing the applicability of the proposed Gamma function (Eq. (17)), whose coefficients were estimated by flume measurements, available fields measurements were used. The analysis demonstrated that a scale factor (equal to 0.7611) is necessary to convert Gamma values obtained by flume measurements into those corresponding to gravel bed rivers. The similitude between flow resistance in a gravel bed flume and in a gravel bed river is governed by the Gamma function and a scale factor, equal to 1.6, is required to upscale the Darcy-Weisbach friction factor values obtained by flume measurements to the river case. In conclusion, the analysis showed that the Darcy-Weisbach friction factor for gravel bed channels can be accurately estimated by the proposed theoretical approach based on a power-velocity profile.