Fluid forces on a closing book

Beach balls bouncing on the floor, airships landing and taking off, and boats floating in shallow water are all systems strongly influenced by the added mass force. As objects move near boundaries restricting fluid flow, the increase in pressure differences creates large forces.

An infinite number of scenarios exist to illustrate the added mass. To facilitate student understanding, however, author James Pantaleone sought a model requiring minimal math and involving forces that are easy to measure. Watching his grandson jumping through puddles, making large splashes of water, he realized that the collision between two flat surfaces is a prime example for teaching about the added mass force.

“When two surfaces collide, the fluid between them is accelerated to large speeds. The math then simplifies because the small amount of high-speed fluid is the most important for the calculations and the rest of the fluid can be neglected,” said author James Pantaleone. “Also, the fluid forces are large and so should be easy to measure.”

The author found that a closing book ejecting air was the ideal example for demonstrating surface collisions in a fluid. The model avoids complex calculations, and the motion of the cover can be measured using a smartphone. Additionally, the changing mass of fluid between the book and the closing cover presents an opportunity to illustrate variable mass systems.

“My hope is that everyone who even glances at this paper will observe this fluid effect for themselves. It only takes a smartphone, a book, and less than a minute to do,” said Pantaleone. “When educators see how straightforward the experiment is, I expect it will be used in their teaching.”

Source: “How the air slows a closing book,” by J. Pantaleone, American Journal of Physics (2023). The article can be accessed at https://doi.org/10.1119/5.0106926 .