Conceptual Errors in Actuator Disc Theory and Betz’s Law for Wind Turbines

This paper started with the explanation of conditions for using momentum equation and presentation actuator disc theory. Focusing on flow model used in disk theory, both Froude-Rankine theorem Betz’s law have been examined. It has found that is not justified because a stream-tube as control volume does really exist (pseudo stream-tube). The also an unfounded velocity (v2) to connect thrust total power loss. Two flaws identified law. First, use unjustified incorrect totally violates condition determining equation. Second, from misinterpreted volumetric rate through disc. These two main lead diverse computational contradictions paradoxes, particularly when considering case impermeable circular become evident applied rectangular plate infinite length. possible solution presented. includes additional consideration energy dissipation downstream disc, similar method calculate Borda-Carnot shock