Abstract Flow in pipe, is a type of hydraulics and fluidmechanics of liquid flow contained by a closed conduit. The dual kind of flow within achannel is open channel flow. This tow types of flow aresimilar in numerous methods, but different in one meam part. The channel flowhave a free surface which is not found in pipeflow. Flow in pipe, being limited within closed channel, does not apply direct atmosphericpressure, but it can concern hydraulic pressure on the channel.

Dimensions ofskin friction and mean-speed profiles have been made in fully developed flowsin pipes and channels in the Reynolds number. These measurements.The measurements by (B. J. McKEON)1.The mean velocity profiles in fully developed turbulent pipe flow are repeatusing a smaller Pitot probe to decline the uncertainties due to velocity gradientcorrections. The other static pressure correction (McKeon & Smits 2002) 3is used in analysing all data and leads to important differences from the(Zagarola & Smits) (ZS) 4 conclusions.

The results verify the presence ofa power-law region near the wall and, for Reynolds numbers bigger than 230×103(R+ >5×103), a logarithmic region further out, but therestrictions of these regions and some of the constants differ from thosereported by (Zagarola & Smits). In special, the log law is found for600

60 ±0.08 and 1.20 ± 0.

1, respectively, with 95%confidence level (compared with 0.436 ± 0.002, 6.15 ±0.08, and 1.51 ± 0.03 found by ZS). In addition,the new data confirm the conclusions by ZS that their pipe flow data are notaffected by surface roughness until the highest Reynolds numbers (ReD >13.

6×106,at a minimum).In the region 350

15R+ forturbulent boundary layers. The values of ? and B reported by ( Osterlund etal). are obviously different, however, from the values given here for the regionof complete similarity which occurs further from the wall, that is for600

1. Background and earlier workB. J. McKEON depenedon the studu of (ZS) to mussuered the fully developed pipe flow for theReynolds number in other range of 200×103 instate of what can be used by the (ZS)on (1998) which is the range of thatfactor is used was 31×103to 35×106 to revise the scale of the meanvelocity profile. They found two overlap regions: A power law for 60

Also, R+ =Ru? /? wherever R is the radius of the pipe (=D/2). Thesefindings be supported by a new scaling argument base on dimensional analysis.In high Reynolds numbers, the scaling for the mean velocity profile in fullydeveloped turbulent pipe flow may be expressed in terms of an inner-layerscaling given by U = f(y, ui, ?,R) (1.1) and an outer-layerscaling given byUc ? U = g (y, u0, ?,R) (1.2) wherever U is the meanvelocity, Uc is the centreline velocity, and f and g denote a functionaldependence.

The inner velocity scale ui is always taken to be u?,but choosing the outer velocity scale u0 is more controversial, as will be seenbelow. Non-dimensionalizing equations (1.1) and (1.2) gives, respectively,