Comprehensive correlating equations that incorporate all of the known theoretical structure, namely, the asymptotic behavior near the wall, the asymptotic behavior near the center line, and the speculative intermediate behavior, have been devised for the local time-averaged velocity and the local time-averaged turbulent shear stress in smooth round tubes. These expressions are postulated to apply directly for parallel plates on the basis of the analogy of MacLeod. The expression for the local time-averaged velocity for smooth surfaces is extended for naturally rough surfaces on the basis of the analogy of Colebrook for the friction factor, while that for the local turbulent shear stress is directly applicable without modification. Separate correlating equations for the time-averaged velocity and the turbulent shear stress are suggested on grounds of convenience and accuracy despite the one-to-one correspondence of these quantities. Correlating equations for the eddy viscosity and the mixing length follow directly but are shown to be redundant.