How to handle the formula for computing net thrust of closely coupled engine systems for an engine with a nacelle that has non-circular dimensions?
In review of my earlier question, @Penguin and my math professor's commentaries agree on the point that the equation $$ Fn= \displaystyle \oint V_x\rho\vec V\cdot\vec n \ dA + \displaystyle \oint(P-P_{\infty})\vec n_x \ dA$$ is the meat of the problem and that when you get the piecewise pressure and velocity, the third term $$- \displaystyle \oint \vec \tau_x \ dA$$ was inconsequential, as it (as far as I can mathematically deduce) describes the core cowl and the external nacelle. As it is an independent characteristic, I'm confident I can just adjust the modelling for a different shape. Thanks again to @Pengiun for providing an outside perspective to my dilemma.