A note on the velocity profile and longitudinal mixing in a broad open channel

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Abstract
The mean velocity profile near the surface of turbulent flow in a broad open channel is discussed with dimensional arguments, and a new empirical constant m is introduced which is analogous to von Kármán's constant for flow near a rigid boundary. It is shown that, while the velocity profile depends only rather weakly on m, the dependence of the coefficient of apparent longitudinal diffusion is stronger, and measurements of diffusion could, in principle, provide an accurate determination of its value. The new profiles for various values of m are compared with those in current use, and finally the correction for finite Reynolds number is discussed.

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