Averaged Navier-Stokes equations with turbulent coefficients and the continuity equation are applied to a theoretical investigation of the effects of inlet swirl velocity on the static characteristics of annular plain seals employed in pumps. The turbulent coefficients are calculated based on the "law of the wall" and Prandtl's mixing length hypothesis. The Navier-Stokes equations and the continuity equation are numerically solved in consideration of the eccentricity of the rotor in the seal. The numerical results show that the inlet swirl velocity significantly influences the circumferential fluid velocity, which increases as the inlet swirl velocity increases in the direction of the rotor spin. For the eccentric seals, this phenomenon enhances the wedge action induced by the circumferential flow, and yields large hydrodynamic fluid-film pressure peaks and tangential fluid-film force. Hence, the effects of the inlet swirl velocity on the fluid-film pressure and the fluid-film force in the seal clearance qualitatively correspond to the effects of the rotor spinning velocity on these characteristics.