An investigation is conducted on the flow in a moderately wide gap between an inner rotating shaft and an outer coaxial fixed tube, with stationary end-walls, by three-dimensional Reynolds-averaged Navier–Stokes (RANS) computational fluid dynamics (CFD), using the realizable $k\u2212\epsilon $ model. This approach provides three-dimensional spatial distributions of static and dynamic pressures that are not directly measurable in experiment by conventional nonintrusive optics-based techniques. The nonuniform pressure main features on the axial and meridional planes appear to be driven by the radial momentum equilibrium of the flow, which is characterized by axisymmetric Taylor vortices over the Taylor number range $2.35\xd7106\u2264Ta\u22646.47\xd7106$. Regularly spaced static and dynamic pressure maxima on the stationary cylinder wall follow the axial stacking of the Taylor vortices and line up with the vortex-induced radial outflow documented in previous work. This new detailed understanding has potential for application to the design of a vertical turbine pump head. Aligning the location where the gauge static pressure (GSP) maximum occurs with the central axis of the delivery pipe could improve the head delivery, the pump mechanical efficiency, the system operation, and control costs.