An extension of von Ka´rma´n’s similarity hypothesis to a cylindrical geometry has been made in order to establish the conditions under which universal velocity similarity will exist for plane-rotating turbulent flows. A characteristic mixing length is found which is proportional to the radial coordinate. From this result and the other similarity conditions obtained, a family of similar velocity profiles is generated which includes the fully turbulent irrotational profile observed by G. I. Taylor in his rotating cylinder experiments. Universal velocity profile and eddy diffusivity laws are also derived, and the universal constant appearing in the equations is evaluated using Taylor’s velocity and wall shear-stress measurements. The universal profile is shown to be that which corresponds to a constant vorticity for the mean fluid motion.