The paper concerns an experimental study of fully developed laminar flow of a Newtonian and non-Newtonian liquid in concentric annuli with combined bulk axial flow and inner cylinder rotation. Pressure losses and skin friction coefficients have been measured for Newtonian fluid, water and non-Newtonian fluids, 0.2% aqueous of sodium carboxymethyl cellulose (CMC) and 5% bentonite solutions, when the inner cylinder rotates at the speed of $0{sim}500$ rpm. The influences of rotation, radius ratio and working fluid on the annular flow field are investigated. And the new correlations among the skin friction coefficient, the Reynolds number and the Rossby number are presented with reasonable limits of accuracy in laminar flow regime.