Despite the advances in the statistical theory of turbulence, the PRANDTL [see 1 of “References” at end of paper] concept of mixing‐length still affords the most convenient method of evaluating momentum‐transfer from velocity‐profiles in turbulent flow. In symmetrical conduits, eddy‐diffusivity is known directly from the BOUSSINESQ quotient of shear‐stress and velocity‐gradient. Hence mixing‐length is not essential for the expression of eddy‐diffusivity in pipe‐flow, but is convenient when the distribution of shear‐stress is not known, as in most flow‐problems in meteorology and hydrology.
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Brooks et al. (1944) studied this question.
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