A general theory of steady three-dimensional flow of nonviscous fluid in subsonic and supersonic turbomachines having arbitrary hub and casing shapes and a finite number of thick blades is presented. The solution of the three-dimensional direct and inverse problem is obtained by investigating an appropriate combination of flows on relative stream surfaces whose intersection with a z-plane either upstream of or somewhere inside the blade row forms a circular arc or a radial line. The equations obtained to describe the fluid flow on these stream surfaces show clearly the approximations involved in ordinary two-dimensional treatments, assuming flow surfaces of revolution or an infinite number of blades. They also lead to a correct solution of the three-dimensional flow in a mathematically two-dimensional manner. A general procedure to solve the direct or inverse three-dimensional problem is described for both subsonic and supersonic flow. The theory is applicable to both irrotational and rotational absolute flow at the inlet of the blade row and at both design and off-design operations.

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