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 :Switch to using the air as a frame of reference, which makes my point easier to understand. Before a wing interacts with the air, the air is still. After a wing interacts with the air, the air is moving, the ""exit velocities"" (velocity when and where pressure returns to ambient) of the components of the affect air will be non-zero. Somewhere during this process, a non-Bernoulli interaction involving some amount of work was peformed on the air, increasing it's total energy.   "