Buoyance Force & Centripital Motion

[Right]

Hello my fellow movers of the Earth!

Could someone who knows better tell me: If a centrifuge were spinning so fast as to produce 1g of centripetal force (net 1g downward + 1g outward), would the bubbles/air in spherical vessels sitting in the centrifuge travel equally inward as upward? Directions relative to the center of the centrifuge.
If so, would the magnitude of buoyant force be √2 of the normal buoyant force (centrifuge off)?

Thanks peeps!

 

[jbriggs444]

If a centrifuge were spinning so fast as to produce 1g of centripetal force (net 1g downward + 1g outward), would the bubbles/air in a spherical vessel travel equally inward as outward?

A spherical vessel? Is this vessel spinning like a top? Or sitting in a spinning centrifuge? Are "inward" and "outward" to be taken with respect to the center of the sphere or the axis of rotation of the centrifuge?

 

[Right]

A spherical vessel? Is this vessel spinning like a top? Or sitting in a spinning centrifuge? Are "inward" and "outward" to be taken with respect to the center of the sphere or the axis of rotation of the centrifuge?

Sorry, that was obscure. Spherical vessel(s) sitting in a spinning centrifuge. And yes, inward with respect to the center of the centrifuge. Will edit for clarity.

And also found a typo - Outward was meant to be upward.

 

[A.T.]

Could someone who knows better tell me: If a centrifuge were spinning so fast as to produce 1g of centripetal force (net 1g downward + 1g outward), would the bubbles/air in spherical vessels sitting in the centrifuge travel equally inward as upward?

Yes.

If so, would the magnitude of buoyant force be √2 of the normal buoyant force (centrifuge off)?!

Yes, but the apparent weight (gravity + centrifugal force) of floating objects or gas bubbles would also be √2 of gravity alone. So they wouldn't submerge less or float faster upwards than normally.

 

[Right]

Yes, but the apparent weight (gravity + centrifugal force) of floating objects or gas bubbles would also be √2 of gravity alone. So they wouldn't submerge less or float faster upwards than normally.

Wonderful, thank you! So it would be correct to say that the magnitude of JUST the upward buoyancy force would remain the same with the centrifuge on or off? I'd also be very grateful for your credentials or basis of knowledge.

 

[jbriggs444]

Yes, but the apparent weight (gravity + centrifugal force) of floating objects or gas bubbles would also be √2 of gravity alone. So they wouldn't submerge less or float faster upwards than normally.

On the contrary. Buoyancy and apparent weight are both multiplied by a factor of $\sqrt{2}$ but inertial mass and viscosity are both unchanged. So falling rocks or rising gas bubbles would move faster than in ordinary one gee gravity.

 

[A.T.]

So it would be correct to say that the magnitude of JUST the upward buoyancy force would remain the same with the centrifuge on or off?

Yes, the vertical component stays the same.

 

[A.T.]

On the contrary. Buoyancy and apparent weight are both multiplied by a factor of $\sqrt{2}$ but inertial mass and viscosity are both unchanged. So falling rocks or rising gas bubbles would move faster than in ordinary one gee gravity.

Yes, right. The difference of buoyancy and apparent weight also would scale by √2, while the resistance to movement and acceleration wouldn't. So they would move faster up/down. But they would not submerge more when floating on the surface.

 

[sophiecentaur]

Off the cuff, I would suggest that bubbles would follow a curved path, tending to vertical at the centre, in addition to the rotation round the axis of spin. A more or less constant upward force and an 'inwards' force proportional to 1/radius of rotation. Just solve the equation of motion. Go on Go on Go on, as Mrs Doyle would say.