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The answer by tpg2114 does a good job of explaining why the loss of energy in the flow due to viscous effects should result in a reduction in lift. I would like to add a few comments about the effective modification of the airfoil shape due to the boundary layer (since the question specifically asked about that). At sufficiently high Reynolds numbers, flows ...


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The general trick is to convert the one second-order differential into two first-order ones. This is done by introducing an extra variable to carry around: \begin{align} \frac{\mathrm dv}{\mathrm dt}&=f(x,\,t)\\ \frac{\mathrm dx}{\mathrm dt}&=v \end{align} for whatever function $f(\cdot)$ you need. This can easily be applied to numerical integration ...


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The easiest way to approach these kinds of questions for me is to forget the equations for a moment and think just in terms of energy and work. In the inviscid case, there is no drag on the airfoil. This means all of the changes in pressure can be used to do something, like create lift. Note: since there isn't anything other than pressure and velocity ...


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