The affinity law is widely used in pump design and experiments. The applicability of the affinity law in an emergency drainage pump at different rotating speeds was studied. Experiments and numerical simulation through ANSYS CFX (Computational Fluid Dynamics X) 15.0 software were used to research the affinity law characteristics. Results show that the simulation of characteristics is basically consistent with the experimental curves. In small flow rate conditions, due to the existence of obvious differential pressure between the pressure side and the suction side in the impeller blade tip area, the leakage flow occurs at the tip clearance, which collides with the main stream at the inlet and generates vortices at the leading edge of the impeller. The tip leakage flows of the pump at four different rotating speeds were compared, and it was found that the tip leakage increased with increasing rotation speed, and at the same rotation speed, the tip leakage flow was large in the small flow rate condition, which led to the simulation value of the characteristics being greater than the scaling value. As the flow rate increased, the anti-cavitation performance of the pump became worse and the hydraulic loss was larger, so the pump’s performance curve deviated from the scaling curve.