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, 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.