Parametric equations are derived that characterize smooth surface profiles for two general classes of nozzles and nonbranching transition ducts: straight sections for axial flow and curved sections (elbows) for in-plane or out-of-plane flow. For each profile, the terminal cross sections are specified as rectangular, elliptical, circular, or a combination of those shapes. At each terminal and in line with the flow, the displacement, slope, and curvature with its respective intersecting uniform section is maintained. Included is a design example of a $90deg$ elbow duct whose cross section remains constant between terminals of elliptical and circular cross sections.

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