On Fluid Dynamics: How does faster movement of fluid reduce pressure? Watch
But if you pinch a waterhose, does not making the path for water to flow through smaller make water flow at a higher pressure, since pressure is the ratio of force to the area over which that force is distributed?
I'm not familiar with Bernoulli's Principle (there is some debate that air speeding up over the top of a wing even matters - Some wings are reflective, so the top side and the bottom side normally produce equal pressures, but the angle of attack of the wing forces the plane up by Newton III)
I think you're just changing variables which aren't so much affected with the plane example.
To do this, consider a stream of fluid moving in a horizontal (geometrical) plane and consider the pressure above and below that plane. The contribution to the overall pressure won't be due to the bulk flow of the fluid, as it's in a different direction - instead it will be due to the random motions of the particles (which can be up or down). So when calculating pressure on a plane wing we are considering pressure due to the random motion of particles, when considering the pressure at the ends of a hose pipe we are considering the pressure due to bulk flow.
Armed with this knowledge we can continue our analysis and apply the law of the conservation of energy. If the bulk motion of the fluid is very fast, for energy to be conserved, the random motion of the particles must be much less. Thus the pressure exerted in vertical directions is much less and in the case of an aeroplane wing you get lift. This can be done mathematically to get the precise result found by Bernoulli.