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Using these results, the inverse problem, which solves for the shape that induces a prescribed pressure, is formulated as a nonlinear boundary value problem with mixed Dirichlet and Neumann surface conditions here, trailing edge shape constraints are directly enforced by controlling jumps in the stream-function or its streamwise derivative through the downstream wake (analogies with potential flows past axisymmetric ringwings showing similar source and vortex interactions are also described). In this paper, both the nonlinear vorticity generation term in Poisson’s disturbance stream-function equation and the Bernoulli constant (which varies from streamline to streamline) are explicitly evaluated in terms of the known plane parallel flow far upstream, recognizing that vorticity convects unstretched and unchanged along streamlines this produces a governing differential equation with an explicitly available right side plus a Bernoulli integral with a true constant fixed throughout the entire flow field. Steady, inviscid, planar and constant density shear flows past thin airfoils have strongly coupled thickness and camber flowfields which can be simply analyzed using some invariant properties of Euler’s equations. Journal of Verification, Validation and Uncertainty Quantification.Journal of Thermal Science and Engineering Applications.Journal of Offshore Mechanics and Arctic Engineering.Journal of Nuclear Engineering and Radiation Science.Journal of Nondestructive Evaluation, Diagnostics and Prognostics of Engineering Systems.Journal of Nanotechnology in Engineering and Medicine.Journal of Micro and Nano-Manufacturing.Journal of Manufacturing Science and Engineering.

Journal of Engineering Materials and Technology.Journal of Engineering for Sustainable Buildings and Cities.Journal of Engineering for Gas Turbines and Power.Journal of Engineering and Science in Medical Diagnostics and Therapy.Journal of Electrochemical Energy Conversion and Storage.

Journal of Dynamic Systems, Measurement, and Control.Journal of Computing and Information Science in Engineering.Journal of Computational and Nonlinear Dynamics.Journal of Autonomous Vehicles and Systems.