Maximum velocity of buoyant object

[ralphamale]

I have a plastic ball 2.75" in diameter weighing 16 grams submerged at 6 feet depth. I am trying to determine the maximum velocity achieved when I release the ball? Also, if I tether (30) balls together with fishing line at 1/2" spacing how will that affect velocity? I really appreciate any help and input on this. Thank you!

 

[Andy Resnick]

Terminal velocity is reached when the buoyant force equals the viscous drag force, which may not occur over the 6 feet. I would start with the full dynamic equation: ma = f_b + f_drag, where f_b is buoyancy and f_d the drag term. Assume Stokes flow for the drag term, and solve for the velocity as a function of depth. You will also have to assume that Stokes flow hold for each sphere in the chain in order to keep this problem easy.

 

[Civilized]

Go to this page and scroll halfway down to read "Terminal velocity in the presence of buoyancy force":

http://en.wikipedia.org/wiki/Terminal_velocity