Further observations on the mean velocity distribution in fully developed pipe flow

Abstract

The measurements by Zagarola & Smits (1998) of mean velocity profiles in fully developed turbulent pipe flow are repeated using a smaller Pitot probe to reduce the uncertainties due to velocity gradient corrections. A new static pressure correction (McKeon & Smits 2002) is used in analysing all data and leads to significant differences from the Zagarola & Smits conclusions. The results confirm the presence of a power-law region near the wall and, for Reynolds numbers greater than 230×10^3 (R+ >5×10^3), a logarithmic region further out, but the limits of these regions and some of the constants differ from those reported by Zagarola & Smits. In particular, the log law is found for 600<y+ <0.12R+ (instead of 600<y+ <0.07R+), and the von Kármán constant κ, the additive constant B for the log law using inner flow scaling, and the additive constant B∗ for the log law using outer scaling are found to be 0.421 ± 0.002, 5.60 ± 0.08 and 1.20 ± 0.10, respectively, with 95% confidence level (compared with 0.436±0.002, 6.15±0.08, and 1.51±0.03 found by Zagarola & Smits). The data also confirm that the pipe flow data for ReD ≤ 13.6×10^6 (as a minimum) are not affected by surface roughness.