blade element momentum theory. mostly from perspective of a propeller in this particular derivation (see my notes for turbine version). linear momentum balance, angular momentum balance, efficiency.

For more detail see the following two references:

Ning, A., “Using Blade Element Momentum Methods with GradientBased Design Optimization,” Structural and Multidisciplinary Optimization, Vol. 64, No. 2, pp. 994–1014, May 2021. doi:10.1007/s00158021028836

Ning, A., “A Simple Solution Method for the Blade Element Momentum Equations with Guaranteed Convergence,” Wind Energy, Vol. 17, No. 9, pp. 1327–1345, Sep. 2014. doi:10.1002/we.1636