A Universal Energy Extraction Limit in Open-Channel Flow

A short theoretical preprint deriving a universal upper bound on extractable energy in open-channel flow, with a strict maximum of 34.52% of the total flow energy attained at Fr = 0.3094. Figure 1 shows the universal energy-extraction limit as a function of the Froude number, with a maximum at Fr ≈ 0.3094. Version 2 changes:– editorial language improvements and clarification of assumptions;– strengthened discussion of limitations and scope;– refined interpretation of the subcritical energetic extremum;– no changes to the analytical results or conclusions.