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Increasing the efficiency of the Engine parts and reduction in development time with good accuracy are the challenges in the Automotive Industry. Lubricating oil pump has been selected for this study. Existing literatures explain the methodology to generate the rotor profile from the given geometrical parameters of the rotor like eccentricity, tooth radius etc. Invariably the specifications to design the pump are provided in terms of pump performance at various operating conditions. The analytical model developed in this study uses the performance and boundary specifications to generate the rotor profile and to estimate the flow rate at various operating conditions of the pump. This methodology includes the generation of trochoidal profile for inner rotor and modified conjugate profile for the outer rotor and the volume calculation of number of chambers (N) which are created between the rotors during meshing.