A CFD study based on unsteady RANS that resolve the gas-liquid interface was performed to examine the unsteady multiphase flow in a liquid-ring pump as a function of its inlet pressure (10, 40, and 80 kPa) and its impeller's rotational speed (1150, 1450, and 1750 rpm). Results obtained show the shape of the liquid ring to play a critical role in creating the expansion ratio needed to draw air into the pump and the compression ratio needed to expel air out of the pump. The dominant processes that determine the shape of the liquid ring was found to be the centrifugal force from rotation, the acceleration and deceleration due to the difference in pressure at the pump's inlet and outlet, and the eccentricity of the impeller relative to the pump's housing. Results are presented to show how the rotational speed of the impeller and the pressure at the pump's inlet affect the nature of the multiphase flow in the pump as well as the pump's effectiveness in creating a vacuum. The effects of heat transfer on the gas phase during the compression and expansion processes were found to be approximated well by polytropic processes. This CFD study was validated by comparing computed with measured volumetric flow rates ingested through the suction port and the torque exerted on the pump's impeller.