Blowing Air across a Paper

Let's take a look!

Watch the video on YouTube.

What kind of experiment is this?

Experimental procedure and explanation:

• When you blow air across the bottom of the paper, the air is deflected downward. This is because the air receives a downward force from the paper. However, the paper is pushed upwards by the air, so the paper rises.
• When air is blown on top of the paper, the paper will not rise much.
• When you lift the downstream side of the paper a little higher, the paper will lift up, becoming almost horizontal. Once the paper becomes horizontal, you could flatten out the upstream side and the paper will remain horizontal.
• By bending the paper in a concave shape, the streamline of flowing air is also bent. While the pressure surrounding the paper is at atmospheric level, the pressure inside the curvature close to the paper is lower, according to the streamline curvature theorem. Therefore, the paper rises. Once the paper rises and becomes stable, the flow will follow the paper and bend downward, receiving a downward force. As a result, there is upward force acting on the paper. At this point, the paper will stay almost horizontal, even if the upstream side of the paper is bent back to horizontal.

[Note]

The explanation that pressure at an area where flow exists is lower (than the ambient pressure) because velocity at that area is higher, in accordance with Bernoulli’s theorem, is incorrect. Even if you blow air with a dryer or with your mouth into an empty space, the pressure will remain almost at the atmospheric level. Bernoulli’s theorem describes the energy conservation law in a fluid. Forcing air to flow increases its energy relative to that of the surrounding air. Therefore, Bernoulli’s theorem cannot be used to compare the moving air with the surrounding, stationary air. Please be careful about this as several books have used this erroneous explanation.

[Keywords]	momentum theory, coanda effect
[Reference]	“The Wonders of Flow” Japan Society of Mechanical Engineering, Kodansha Blue Backs pp. 128-133