On the incomplete similarity for turbulent velocity profiles in rough pipes

The possibility of extending Barenblatt's hypothesis of incomplete similari ty for the velocity profile is analyzed for rough-pipe flows. The verificat ion of this hypothesis, which leads to a power law in the intermediate regi on of the flow, is performed using Nikuradse's well-known data for pipes wi th homogeneous sand roughness. As detailed comparison between the log law a nd the power law would require much higher measurement resolution, no attem pt is made here to assess the validity of one or the other law, and the pow er law profile is simply used as a working hypothesis. The power law fits w ell for a large part of the pipe section both for the transitionally rough regime and the fully rough regime. The coefficients of the power law show a n interesting behavior as a function of the Reynolds number and the relativ e roughness. For the fully rough regime, it is possible to obtain simple ex pressions for the power law coefficients and the resistance law. (C) 2001 A merican Institute of Physics.