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Three-dimensional transient computations of flow in variable-displacement vane pumps and in gear pumps have been completed. Several innovations were required for this new application of computational fluid dynamics (CFD). New physical insight into the pumping process has been extracted by exercising the model. Likely cavitation sites have been identified, the importance of fluid compressibility has been established, and reductions in flow losses and noise have been realized. Based on these computations, design changes have been proposed and evaluated in hardware for automatic transmission variable- displacement vane pumps. The same methodology is being applied to fixed- displacement gear pumps. These findings have relevance to both the Transmission Designer and the Transmission Analyst.