The theory of three-dimensional flow in axial turbomachines was extended to include the effects of variable hub and tip radii such as occur in the entrance stages of conventional axial flow compressors and, to a larger extent, in mixed flow compressors. The problem is simplified by assuming an infinite number of infinitely thin blades in each blade row, so that axially symmetric fluid motion results.The effect of variable hub and tip radii of the annulus walls is investigated when the tangential velocities are small but arbitrary, and when they are large but of special form. The combined effect of heavily loaded inlet guide vanes and variable hub radius is also investigated for the case in which the inlet guide vanes impart a motion very nearly of the solid-body type. The boundary conditions for the variable hub radius require linearization, thus restricting the magnitude of perturbation to be induced by the wall. Finally, the effect of a loaded blade row placed behind the inlet guide vane is determined.The local axial and tangential velocities induced by the variable wall radius were found to be of the same general magnitude as the velocities induced by a normal rotor or stator blade row. Although the forms of the solutions are somewhat complex for routine application in turbomachine design, a sufficiently simple approximate result is obtained for one case and it is indicated how the method of approximation may be extended.
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