Re: Why do solids move to centre in a whirlpool but to edges of a centrifuge ?

Jocelyn,

I can understand your difficulty--I got dizzy working this out! What confused me to start was that centripetal force is important to both a centrifuge and a whirlpool, so I was focused on that. But in the whirlpool, the force moving the solids toward the center is unrelated to the rotation: it's the larger-scale motion of the fluid towards the drain.

That may be enough to answer your question, but I'll elaborate. (You might know all of this, but not everyone who might read this teaches physics, so bear with me.)

First the centrifuge. Imagine a blob of solid is sitting in a less dense liquid in the centrifuge. When the centrifuge starts, both the solid and the liquid are accelerated forward, and tend to move in a straight line. But their platform is moving in a circle, and that straight line is directed toward the outside of the circle. Unless some other force pushes them back toward the center, both liquid and solid will move to the outside of the centrifuge.

The force toward the center which is required to keep the solid and liquid in a circular path is given the name "centripetal force", and how large the centripetal force F must be to keep a blob of unit volume moving in a circle depends on the blob's density d and speed v, and the radius r of the circle:

On to whirlpools. I've never seen solids separated from liquids in a whirlpool, so here I'm guessing about the technique. In a laboratory, or a bathtub or a brewery, whirlpools form as fluid is drained out of a hole. (This is not the only way to form whilrlpools, as evidenced by tornadoes. More information about how vortices form appears in another previous MSN answer.) The fluid flows toward the hole from all directions, carrying solids with it. Once the solids reach the hole they might drain out, or they might stay there, but they won't float back into the fluid since there is no flow away from the hole to carry them.

Centripetal force enters the picture as follows: as the water spins down the whirlpool toward the drain, it is moving in a circle. As we know, some force toward the center of the circle must be acting on the fluid, or its path would straighten. In the case of the whirlpool, the centripetal force is provided by the pressure difference between the gap in the center of the whirlpool (where the pressure is low) and the interior of the fluid (where the pressure is high, owing to the weight of the fluid). Thus it is the pressure, acting as centripetal force, which maintains the circular motion of the whirlpool. But this force does not move solids toward the whirlpool.

Another interesting example of the application of centripetal forces is provided by carnival rides: see the previous MSN question about loops and corkscrews.

Hope this is satisfactory. Enjoy the summer! For a more detailed explanation of why things move toward whirlpools, see the MSN posting about why particles move toward the center in a cup.

Dan Goldner (goldner@mit.edu)
MIT/Woods Hole Joint Program in Oceanography