Significance A new explicit formula for estimating the friction factor using six parameters is proposed. The model was set up by considering the effect of residual stresses in the flow by two distinct contributions: the first is attributed to the flow velocity (Reynolds number) and the second to the duct roughness. Compared to other models, this new equation gives the best fit with Nikuradse's results. A new model to calculate the friction is proposed. The model is based on assuming the residual stresses due to the laminar to turbulent flow transition by two distinct contributions: the first is attributed to the flow velocity (Reynolds number) and the second to the duct roughness. Compared to other models, this new equation gives the best fit with respect of Nikuradse's results. The model does not consider the effect of pipe wall on the velocity distribution.
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Díaz–Damacillo et al. (2019) studied this question.
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