LAUSR

Abstract Previous studies demonstrated that for open channel flows the power velocity profile can be integrated to obtain the flow resistance law. In this paper the relationship between Γ coefficient of the power velocity distribution, the channel slope and Froude number (Eq. (9) ) is firstly presented. Then the measurements carried out in a laboratory flume covered by hemispheric elements for two different hydraulic conditions (partially inundated and inundated) are used to calibrate this relationship. These elements are placed with a square arrangement and have a concentration range 4–64%. For the two investigated hydraulic conditions, this analysis demonstrates that the relationship to estimate the coefficient of the velocity profile is characterized by the same exponent of slope and Froude number while a different scale factor a has to be used. The effect of roughness element concentration Ch on flow resistance is also studied by the calibration of Eq. (9) for each experimental series characterized by a single value of Ch. For the partially inundated condition and values of the roughness element concentration less than 25%, the coefficient a increases with Ch while for Ch values ranging from 25 to 64% a decreases with concentration. For the submerged condition, the coefficient a increases with Ch and results almost constant for concentration values greater than 49%. The variability of the coefficient a with Ch is the effect of the variability of the reference plane for the water depth measurement with the concentration. Finally, the obtained relationships to estimate Γ function and the theoretical flow resistance law are verified by 205 measurements carried out in gravel bed rivers. In conclusion, the developed analysis demonstrates that an accurate estimate of the friction factor can be obtained for the investigated gravel surfaces by the proposed flow resistance equation and the obtained relationship to estimate Γ function.