Power law and log law velocity profiles in fully developed turbulent pipe flow: equivalent relations at large Reynolds numbers

The classical two layers (the inner and outer layers) from open equations o f mean turbulent motion, in a fully developed pipe flow, at large Reynolds number in MMX are matched by the application of the Millikan-Kolmogorov hyp othesis. In the overlap region, the classical solution of the open function al equation for the velocity profile is the log law region. It is shown her e that the open functional equation also possesses another functional solut ion, the power law velocity profile in the overlap region. The non-unique n ature of the solution of the open functional equation predicts both a power law and log law velocity profile. At large Reynolds number the equivalence of the power law and log law is analysed. The comparison of the theory wit h classical data of Nikuradse and super-pipe data of Zagarola is encouragin g.