Making use of functional variations with variable domain and natural boundary conditions, this paper presents a unified theory of various hybrid problems (being a unification as well as a generalization of direct and inverse problems) for three-dimensional incompressible potential flow in a rotor blading. Three families of variational principles (VPs) have been established and provide a series of new rational ways for blade design and a sound theoretical basis for the finite element method (FEM). This theory can be extended to compressible and rotational flows and also constitutes an important part of the optimum design theory of bladings [8].

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