It is shown that Von Karman's similarity hypothesis can be used to deduce the Reynolds number dependence of the nor-dimensional turbulent velocity profile in both the circular tube and parallel plate channel. The analysis uses a two part model of a sub-layer and a main stream and ensures that there are no discontinuities in the profile gradient and that it fulfils the correct centre-line boundary condition. There is good agreement with experimental results in both configurations.
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Alan Quarmby (1969) studied this question.
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