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The Bernoulli principle is a restatement of the conservation of momentum. The energy of a stream of air is shared between pressure energy (due to random molecular collisions) and stream flow energy (the shared component of the molecular motion in the direction of the stream). As the air moves around the wing, it is forced to speed up because of mass conservation. The stream flow energy thus increases, and since the total energy has to remain constant (energy conservation), this must come at the expense of the random molecular energy or pressure. Therefore, the pressure must drop the faster the stream is accelerated.