Abstract: The influence of the shape-factor and pitch-circle radius of the conjugate rotor,as exemplified in a typical 3-lob circular arc rotor-pump,on the volume utilization rate and radial/axial/conjugate internal leakage rates was empirically approximated,mathematically formulated with the equivalent cylindrical-planar surfaces gap model and theoretically analyzed.The leakage rates can be derived by calculating the equivalent curvature radius of the gap instead.The calculated results show that the shape-factor and pitch-circle radius have a major impact.For example,as the shape-factor increases,the volume utilization rate rapidly and radial leakage rate slowly increase,and the conjugate leakage rate decreases,accompanied by a fast decreasing impact of the pitch-circle radius;as the pitch-circle radius increases,the radial/axial/conjugate leakage rates decrease.We suggest that the volume utilization efficiency may be optimized by maximizing the top radius of conjugate rotor.