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I need to design a controllable Bernoulli ball airflow levitation setup.

For context, the ball will be about 80 mm in diameter, and I need to be able to operate the height in range from zero to one meter from the air outlet.

What equations can be used to compute height vs airflow and outlet geometry?

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I would try using the drag equation to determine the force on the ball. You have the capability to vary air speed, which would change the drag.

I think the hard part you would have trying to do this would be to characterize the air velocity as a function of distance from the source and angle from the axis of the source. If you assumed the air velocity was constant along the axis, then congratulations - you made a blowgun.

I think you would have so much difficulty that you would be better if trying to determine the air velocity - height relationship empirically and then trying to fit a curve to that data.

You could even take those empirical results, use the drag equation, and see if that will give you wind speed by distance.

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