New, more accurate values for the time-averaged velocity distribution and the mixed-mean velocity (and thereby the friction factor) were obtained for fully developed turbulent flow in annuli by numerical integration of the equations of conservation using a theoretically based correlating equation for the turbulent shear stress. These computed values are represented almost exactly by simple algebraic equations that may be considered to be predictive rather than correlative because they have a theoretical structure, are virtually free from empiricism, and are not based on the calculated values. These predictive expressions agree closely with the most reliable experimental data within their scatter. (C) 2003 Elsevier Ltd. All rights reserved.