Consider this aerofoil. Let the leftmost point be S and rightmost point be E. Let the topmost point be T and a point on the bottom of the foil be B. Let the wind blow as shown in the figure above. Bernoulli's principle says that the air blowing along S-T-E must travel a path longer than than that travelled by air blowing along S-B-E, and for the time taken to reach E must be the same, the wind blowing through the top of the foil must have a higher velocity and hence the pressure on the top of the foil is lesser than that on the bottom part of the foil and hence the plane takes off. But, why should the air blowing along S-T-E and S-T-B take the same time to reach E? Let me frame this question in a different way. Consider two particles in air coming towards the foil, one which will take the path S-T-E (for convenience sake let this be particle 1) and the other which will take the path S-B-E (let this be 2). Until they reach the foil, they have the same velocities. But after they reach the foil, either particle 1 speeds up, or particle 2 slows down, or both happen. Thus, at least one of them accelerates. According to Newton's first law, which says that no object accelerates unless an external force is applied, there must be a force acting on this particle. Where does this force arise from and for what reason does it arise?