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

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\,×\,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.