Further Thoughts on Turbulent Flow in a Pipe

Nikuradse’s 1932 paper on turbulent flow in a smooth pipe contains a wealth of information on flow resistance (friction factor) and profiles of velocity and eddy viscosity. The goal here is to study this information in detail with the objective of applying it to other turbulent-flow situations. In particular, reverse engineering supports a value of n = 2 for the exponent on the volumetric dissipation in the decay term of the equation of the dissipation theorem. Of equal importance, integration of Nikuradse’s profiles of eddy viscosity does not lead to his formula for the universal resistance law; instead the presence of the viscous sublayer has an overt effect on the result even though we had thought that such a region influenced only the form of mass transfer at high values of the Schmidt number. A formula is proposed for the decay of dissipation for turbulent flow in smooth pipes.