Several generations of engineers have found that the one-dimensional approach to compressible fluid flows in ducts is extremely informative and effective. This paper extends these methods to axisymmetric flows so that they may be used to understand and estimate the behavior of azimuthally unrestrained, swirling flows. The already-established understanding of duct flows makes an elaborate investigation of the new results unnecessary. The paper contains the underlying assumptions and resulting equations, an outline of the solution technique, a comprehensive table of influence coefficients, and a variety of interesting examples peculiar to swirling flows drawn from the field of rotating machinery.

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