It is shown that slow hydrodynamic flow with velocities of a few millimeters per second reduces the spin-lattice relaxation rate of fluids confined to pores of a diamagnetic, polar, solid material. The effect is predicted by an analytical theory and Monte Carlo simulations of model pore spaces. Adsorbate molecules diffusing in the vicinity of pore surfaces can perform adsorption, desorption, and readsorption cycles, effectively leading to displacements along the surface (also termed "bulk mediated surface diffusion" or BMSD). Since the surface determines the orientation of the adsorbed molecule relative to the external magnetic field, desorption at one site and readsorption at another site of a nonplanar surface will cause molecular reorientation. This is the basis of the "reorientation mediated by translational displacements" (RMTD) relaxation mechanism. If hydrodynamic flow is superimposed on diffusion, the RMTD process will be accelerated in a sort of rotational analog to translational hydrodynamic (or Taylor-Aris) dispersion. This reveals itself by a prolongation of spin-lattice relaxation times at low frequencies. The flow-relaxation effect takes place in the vicinity of the pore surfaces on the order of nanometers. The conclusions are (i) the BMSD and RMTD relaxation mechanism of fluids in porous materials is corroborated, (ii) hydrodynamic dispersion affects molecular displacements at surfaces, and (iii) interfacial slip in the sense of a molecular hopping, i.e., a desorption-readsorption process takes place.