Why Does a Ball Stay Stationary in a High-Speed Air Stream?

[Darkalyan]

Homework Statement

This isn't a homework question, but more like a theory question that my teacher and I are having trouble figuring out. We're trying to figure out why this ball, more or less, stays still in a high speed stream of air:

http://laserpablo.com/videos/videofiles/Bernoulli.htm

Homework Equations

Bernoulli's Principle, gravity, balancing vector diagrams.

The Attempt at a Solution

The stream of air is going from the bottom/left to the top/right, and we had a couple theories. I think the ball is spinning clockwise, and bernoulli's is causing a lift perpendicular to the stream. The force of gravity is acting down, and the reason there isn't a net movement to the left is because the stream itself pushes the ball to the right. Therefore, the forces cancel out and the ball, more or less, stays still. However, my professor thinks the ball is actually spinning counterclockwise, and in that case Bernoulli's wouldn't explain why the ball is floating in midair; it would actually cause the ball to be pushed downward, correct? Is there something we're missing here? What're your thoughts?

 

[vigintitres]

The only thing I know that I can say about it is that Bernoulli's doesn't actually apply because of all kinds of viscous effects, but instead you'd have to apply the momentum equation (one of the navier-stokes equations) and also/alternatively you could apply the energy equation, but you definitely can't use Bernoulli because of the presence of viscous boundary layers around the ball. Navier-stokes would be able to tell you what is going on since they are partial differential vector equations, but in order to use those navier-stokes equations you'd really have to run a computer simulation and numerically evaluate the equations because of the inherit complexity of those partial derivatives.

 

[kerimek]

I would say that both theories have some validity. Bernoulli's Principle states that as the speed of a fluid increases, the pressure decreases. In this case, the high speed stream of air is creating a region of low pressure above the ball, causing it to be lifted. This lift force, combined with the force of gravity acting downwards, creates a balancing effect and allows the ball to stay still in the air.

However, the direction of spin of the ball does play a role in this scenario. If the ball is spinning clockwise, as you suggested, it would create a gyroscopic effect that would help stabilize the ball in the air. On the other hand, if the ball is spinning counterclockwise, it would create a destabilizing effect and could potentially cause the ball to fall.

In either case, the key factor here is the balance of forces. The lift force from Bernoulli's Principle, combined with the spin and gyroscopic effects, must be enough to counteract the force of gravity and keep the ball in place. It would be helpful to conduct further experiments or simulations to determine the exact forces at play in this scenario.