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Abstract: The scaling and similarity of wall bounded turbulent flow were studied. The properties of such flows and the relationship between a power law and a logarithmic type of velocity distribution were investigated. Based on the physical mechanism involved, our results show that the power law and the logarithmic distribution are only different forms with the same hypothesis and hold only in the outer flow zone. Thus, a universal explanation for various empirical formulae of velocity distribution was obtained. Manning’s formula was studied to explain theoretically the experiential result that the roughness coefficient is only a comprehensive parameter of the whole system without a corresponding physical factor. The physical mechanism of the velocity distribution of parallel to wall bounded flow was explored, the results show that the parameters in the formula of velocity distribution are indices of the system responding to flowing environmental factors to represent general case of boundary roughness and the flowing state, corresponding physical mechanism is vortex motion.

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