It is commonly assumed that for turbulent flow in annuli the radii of zero shear and maximum velocity are coincident. By inspection of the differential equations for such flow and by an integral analysis it is shown that this is not necessarily true. To check whether important differences could occur, experiments were made in which velocity and shear stress distributions were measured in one smooth and two partially rough annuli. The results show no difference in the radii for the smooth annulus, but for the partially rough annuli there was a small but significant difference. This difference explains the breakdown of Hall's transformation theory reported by other investigators. The error introduced by use of Hall's theory is however small, of the order of 10 % or less.