The endoreversible thermodynamic theory of heat engines is extended to fluid flow power converters. The useful power can be extracted from the piston and cylinder apparatus. The correlation between power output and efficiency is derived based on a linear flow resistance relationship. The influences of the piston-cylinder friction and nonlinear flow resistance relationships on the performance of the converter are also analyzed in this paper. Performance optimization is undertaken based on the overall size constraints. The paper also develops an analogy among the fluid flow power converters, endoreversible heat engines, endoreversible isothermal chemical engines, classical reversible heat engines, and the ideal motor powered by electrical battery. The results can be applied to the performance analyses and optimization for many steady-flow shaft-powered components.