We derive the upper limit for power extraction from an open-channel flow with lateral bypass representing tidal power or run-of-river plants for the complete range of blockage σ , Froude number Fr 2 and turbine head H T . For this, a generic turbine model is used: a momentum and energy sink distributed over the geometric blocking σ of the channel allowing lateral bypass. It is indicated that existing models neglect important aspects of the free-surface deformation due to the energy extraction,

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... ielding unphysical behaviour at high blockage, high Froude number or high turbine head. The asymptotic validity of existing theories for σ → 0, Fr 2 → 0, H T → 0 becomes evident: firstly, by comparing existing theories with the presented general theory; and secondly, by the experimental validation of the existing and presented theories. The accompanying systematic experimental study comprises a wide range of blockage ratios, 0.25 σ 1.0, of downstream Froude numbers, 0.2 Fr 2 0.5, and of different turbine heads, H T , measured in multiples of the specific energy E 0 of the undisturbed flow. The subsequent model-based optimisation allows an indication of the optimal turbine head H T,opt /E 0 as well as the maximal obtainable coefficient of performance C P,opt as a function of σ and Fr 2 or downstream water depth h 2 /E 0 , respectively. The theory reveals points of operation in which there is a surge wave in the tailwater. The new physical insight and optimisation results may serve for plant design and operation, as well as for investment decisions.