Taylor–Couette–Poiseuille (TCP) flow dominates the inner water-cooling circulation of canned motor reactor coolant pumps. Current research on TCP flow focuses on torque behaviors and flow regime transitions through experiments and simulations. However, research on axial flow resistance in a large Reynolds number turbulent state is not sufficient, especially for the various flow patterns. This study is devoted to investigating the influence of annular flow on the axial flow resistance of liquid in the coaxial cylinders of the stator and rotor in canned motor reactor coolant pumps, and predicting the coolant flow distribution between the upper coil cooling loop and lower bearing lubricating loop for safe operation. The axial flow resistance, coupled with the annular rotation, is experimentally investigated at a flow rate with an axial Reynolds number, Rea, from 2.6 × 103 to 6.0 × 103 and rotational Reynolds number, Ret, from 1.6 × 104 to 4.0 × 104. It is revealed that the axial flow frictional coefficient varies against the axial flow rate in linear relation sets with logarithmic coordinates, which shift up when the flow has a higher Ret. Further examination of the axial flow resistance, with the Rea extending to 3.5 × 105 and Ret up to 1.6 × 105, by simulation shows gentle variation rates in the axial flow frictional coefficients against the Rea. The relation curves with different Ret values converge when the Rea exceeds 3.5 × 105. A prediction model for TCP flow consisting of a polygonal approximation with logarithmic coordinates is developed to estimate the axial flow resistance against different axial and rotational Reynolds numbers for the evaluation of heat and mass transfer during transition states and the engineering design of the canned motor chamber structure.