# Ball Floating on Air Stream

1. Sep 23, 2013

### BenB8691

Hi all,

I am working on a prototype and I have a question that I am not sure how to answer, thus the reason I am here.

I have a piece of 4" pipe that I will vertically mount and I am reducing down to 1". Inside the tubing I have a racquetball. I am going to be sending air through the pipe and I want to know how to calculate at what flow rates the ball will float on the air and how high the ball will go.

I know the inside diameter of the pipe is 4" and the ball is 2.25". I am guessing I will need the weight of the ball, but I don't know of an equation that will tell me the following: 1.) How much air is required to lift the ball inside of the pipe? and 2.) How high the ball with varying amounts of air passing through the tube?

Can anyone help me with this? Any help is greatly appreciated.

Thank you,
BenB8691

2. Sep 23, 2013

### jbriggs444

If the vertical tube is uniform then if the racket ball lifts at all it will go all the way to the top and stick in the outlet hole.

How fast the air needs to be moving to make this happen seems to me to be a matter for experiment. Turn it on and see.

3. Sep 23, 2013

### AlephZero

You can get a rough estimate of the air velocity be saying that the drag force on the sphere (see http://en.wikipedia.org/wiki/Drag_coefficient) equals its weight.

But since the ball is blocking about 30% of the area of the pipe, that will change the air flow pattern around the ball and the assumptions in the drag calculation won't very accurate.

As jbriggs said, if the pipe has a uniform diameter you won't be able to get the ball in a stable position part way along the pipe, unless you do something like make small holes along the length of the pipe to leak some of the air out, so the air velocity at the top is smaller than at the bottom.

4. Sep 23, 2013