Modified log-wake laws for turbulent flow of the outer and inner regions in smooth pipes

Based on theoretical analysis two modified log-wake laws for turbulent flow in smooth pipes are obtained, one is applicable to the outer region and other one to inner region, the new law for the outer region fits the velocity profile measured in smooth pipes by Zagarola very well and the effect of Reynolds number can be taken into consideration, the velocity profile for inner region satisfies the wall boundary conditions, equals zero at the pipe wall and smoothly joins up with the velocity profile in outer region, the adopted eddy viscosity model is consistent with Laufer's, Nunner's and Reichardt's experimental data.