One thing to keep in mind about Bernoulli's Law. It is an application of the law of energy conservation. As such, it can be misapplied. In particular, it can be misapplied if energy is added or removed from the system in question.
Try this experiment. Take a piece of paper and hold it horizontally in front of your mouth, hanging down. Blow across the top of it--you will see it flutter up. Now blow across the bottom of it--and it will still flutter up. Why doesn't it flutter down? Now hold it vertically downward and blow across the top of it--it doesn't move at all. Why not? Where is the Bernoulli effect?
The answer to this question is that the increased kinetic energy from the higher air velocity does not need to be compensated by a drop in potential energy (lowered pressure), because you are adding energy to the system by blowing on it. So the pressure stays the same, and the speed increases. Energy is not conserved, so Bernoulli doesn't work.
Now consider a venturi, such as can be found in a carburetor or a spray bottle for household cleaners. These devices do not work without a venturi. A venturi is a double-ended funnel that squeezes the air and then releases it. Clearly the Bernoulli effect is what makes these devices work. How? The moving air itself is not enough, because again the increased velocity is caused by energy added to the system. But a venturi, now that is something different. The venturi funnel is able to change the velocity of the air without changing the energy of the air. Since the force of the funnel walls is applied perpendicular to the airflow, no energy is added that way. And since the air in question is incompressible, it must travel faster down the narrow venturi throat. This increased kinetic energy must come from somewhere, and in fact it comes from the potential pressure energy. So pressure drops. Here is a real example of the Bernoulli effect at work.
