For preliminary design of compressor transition ducts, knowledge-based tools for the rapid assessment of aerodynamic performance of S-shaped ducts are not currently available in the open literature. This is due to the highly complex flow developing under the combined influence of pressure gradients and streamline curvature. This paper presents a new approach enabling an agile design process avoiding premature use of time-consuming high-fidelity CFD calculations. The features of a 2D axisymmetric incompressible steady flow field are captured with a semi-analytical viscous inviscid interaction method. A potential core, based on streamline curvature and implicit velocity profile by parametric spline reconstruction, is coupled to an integral method predicting the turbulent boundary layer growth up to separation. The shear stress distribution is generated by a modified mixing length model for strongly curved flows and wall shear stress closure is performed by inverse calculation of a composite law-of-the-wall. When compared to CFD, the aerodynamic loading is generally predicted to within ±3% but convergence is achieved 20 times faster.