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Bernoulli's principle

Ellipsoidal object in a fluid flow

Stream lines and resulting force for a fluid flow around an elliptical cylinder (air wing). The flow streams from the left to the right in the picture. Places where the density of stream lines is large correspond to high average speed of the fluid molecules and vice versa.

When we go around the surface of the ellips, then we find places where the density of streamlines is larger and other places where that density is smaller. This may give us an idea of how the pressure on the surface varies from place to place. Places where the density of streamlines is large indicate that the speed is high there and consequently, according to Bernoulli's principle, the pressure low. On the other hand, at places where the density of streamlines is lower, the pressure is higher.
When we add all forces on the surface of the ellips, then we obtain a resultant force as indicate by F in the streamline picture. Furthermore, the force F does not act in the center of the ellips, but at a distance a from the center. When, moreover, the center of mass of the plane coincides with the center of the ellips, this results in a momentum a×F which is the main reason for airplanes to take off.

ping-pong ball in an airstream