Re: how can i use bernoullis principle to explain the following.

I'm not sure I understand the question completely but I will try to answer. I find Bernoulli's principle a little unsatisfactory like a number of principles which are described in a way which doesn't really explain why things happen but just says they do. So when the principle is described as " a fluid which flows quickly exerts less pressure than one which flows slowly" I want to know why!

In the case of an aircraft wing, the shape is such that the air going over the top of the wing travels further than the air going underneath. That means that by the time the two airflows are re-united behind the wing the air going over the top has travelled faster because it has had to go further. Using Bernoullis principle we can expect the wing to feel a higher pressure from underneath than on top, so on balance, the wing experiences an up-ward force from the air which counteracts the gravitational force. The aircraft can therefore fly.

However we still havn't really found out why. One way of looking at it is that the air going over the top occupies a bigger volume because it is stretched over a greater distance. However, there may be a better way to look at it. The shape of the wing deflects the air going over the top slightly upwards and then the surface of the wing drops away. The inertia of the air flow tend to take the air away from the wing leaving a low pressure region above the back part ot the wing. Underneath the wing the air is directed against the back part of the wing and exerts a higher pressure as it is deflected downwards. Using this type of picture and the fact that gases consist of molecules which have mass and movement, it is easy to see how the low-pressure region above the wing and the high pressure region below the wing are produced. The net effect is an upward force.

Let's look at the "ballon" in the hair dryer. I used a table-tennis ball. If you point the air flow upwards the ball is lifted up by the flow of air hitting the ball from below. The air is deflected round the ball leaving a low pressure region above the ball as it sweeps past. That's easy to picture. What is a little more difficult to understand is why the ball doesn't fall when it moves a little sideways. Here, it is probably worth looking at an extreme position.

If you tilt the dryer so that the flow is at an angle to the vertical, say about 30 degrees. Let us say the dryer is on the right of the ball. The ball can be held stationary in the air to the left side of the dryer just underneath the flow of air. The forces acting on the ball are all in equilibrium since the ball does not move. Why isn't it pushed sideways. The air is flowing sideways as well as upwards. It is much easier to explain with a diagram but the secret is that the flow of air is faster above the ball than below and faster on the right hand side of the ball than the left. As with the wing, the flow of air over the ball is deflected away from the ball and creates a low pressure region on the far side of the ball from the dryer but this low pressure region is on the right side of the ball. The ball would tend to move towards this low pressure area so there is a force which we can describe by an arrow pointing up and to the right. Another force would be expected to be acting upwards and to the left due to the impact of the airflow in the direction from the dryer to the ball.

The forces the the left and to the right are equal. The ball makes sure of that by settling into a position relative to the airflow where this is the case. The othe force is gravity. The forces exerted by the air have components which point upwards and these oppose gravity. Again the ball settles to a point vertically were that is the case.

Try it! It does work. You can explain why, when the airflow is vertical, you can pull the ball a litle way out of the stream and it will pop back into the middle.

It's all a question of colliding molecules ! The fast ones tend to pull others into the stream by knocking them in the direction of flow.