Blowing Air over a U-shaped Piece of Paper

Let's take a look!

Watch the video on YouTube.

What kind of experiment is this?

Experimental procedure and explanation:

• Fold a thick paper (such as a postcard) into a “U” shape and place it on a table.
• Blow air between the paper and the table. The paper will not be blown away. Instead, it will be pulled down against the table.
• This phenomenon can be explained by flow separation or boundary layer separation.
• In some cases, as shown in the diagram, flow separation occurs and a recirculation zone appears. This separated zone narrows the flow path, and as a result, the flow velocity increases. The velocity is greater here than it is upstream (at ambient pressure), and thus the pressure decreases (According to Bernoulli’s theorem, the pressure energy decreases by the same amount as the increase in kinetic energy). Consequently, the paper will be pulled down against the table.
• In some other cases, separation might not occur. In such cases, a boundary layer where velocity is smaller forms along the paper; this narrows the flow path, thereby increasing the flow velocity away from the paper and reducing the pressure. Consequently, the paper will still be pulled down against the table.

[Note]	An incorrect explanation in accordance with Bernoulli's theorem exists; that is, the pressure at an area where flow exists is lower (than the ambient pressure) because velocity there is higher. 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]	Flow separation, boundary layer, Bernoulli’s theorem
[Reference]	“Illustrated Fluid Dynamics Trivia,” by Ryozo Ishiwata, Natsume Publishing, pp. 208-209 “The Mysteries of Flow,” Japan Society of Mechanical Engineering, Koudansha Blue Backs, pp. 136-139