Work Extraction from Fluid Flow: The Analog of Carnot's Efficiency

Aiming to explore physical limits of wind turbines, we develop a model for determining the work extractable from a compressible fluid flow. The model employs conservation of mass, energy, and entropy and leads to a universal bound for the efficiency of the work extractable from kinetic energy. The bound is reached for a sufficiently slow, weakly forced quasi-one-dimensional, dissipationless flow. In several respects the bound is similar to the Carnot limit for the efficiency of heat engines. More generally, we show that the maximum work-extraction demands a contribution from the enthalpy, and is reached for sonic output velocities and strong forcing.