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

The measurements by Zagarola and 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 × 10³ (R⁺ > 5 × 10³), 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 Re_D ≤ 13.6 × 10⁶ (as a minimum) are not affected by surface roughness.