The authors have made an experimental study of the fluid-mechanical and transport properties of a system in which a stream of air flows axially in the long annulus between a rotating cylinder and a stationary coaxial outer tube. The fluid mechanical investigations were aimed at elucidating the nature of the flow in, and the stability limits for, the laminar + vortex flow regime. Only a part of these results, relating to the criteria for transition between the laminar and laminar + vortex flow regimes, is outlined in this paper, which is divided into two parts. Part I deals chiefly with the measurement of mass and momentum transfer rates from the walls to the stream in the laminar + vortex regime. In Part II an apparent dissimilarity between these mass and momentum transfer results is discussed. Over the range of axial flows, rotor speeds and annular widths studied, it is concluded that the laminar/laminar + vortex transition is significantly affected by only two dimensionless groups, viz. Re z ≡ V zb/v and Ta ≡ V φ b/ν√ b/r 1‡. It appears that the latter group can advantageously replace previous, more complicated, formulations of the Taylor number in all fluid stability and transport correlations for rotating cylinder systems. Mass transfer rates were measured chiefly in a wetted wall apparatus, using water or n-heptane, and in a mercury-transfer system from a solid surface of silver amalgam. Four different values of b/r 1 were used in this set of experiments, whose results could be correlated over the entire range of experimental conditions (within the laminar + vortex regime) by an expression of the form Sh f(Re z, Ta, Sc ). Rates of axial momentum transfer were determined from axial pressure-drop measurements. It appears that the results can be correlated over the whole range of flow conditions and for two different values of b/r 1 in terms of three dimensionless groups, viz. pressure drop enhancement over that for laminar flow, Re z and Ta; but there are indications that b/r 1 may enter additionally into the correlation.