Shape of a bubble inside a rotating container

[Raihan amin]

1.

A closed cylindrical vessel filled with water (at room temperature) contains a small air bubble of normal pressure and volume $V=1~{cm}^3$ inside in it.The cylinder is then started to be rotated slowly with a small angular acceleration in a complete weightlessness (at a space station) .When the angular velocity of the cylinder has reached to $w_0=30~s^{-1}$,it is kept constant.
Find the stationary shape of the air bubble.The surface tension of the water is $\sigma=0.7~ N/m$.
The extra pressure inside a bubble is related to the surface tension is as follows:
$$∆P=\frac{2\sigma}{R}$$.
And for cylindrical symmetry, the pressure inside the container will be
$$P=\frac{1}{2}{\rho}w^2r^2$$

From V we can find $R_0$.
But i can't figure out how the velocity of water particle will affect the shape of the bubble and what is the advantage of weightlessness?
Thanks.

 

[kuruman]

The advantage of weightlessness is that you don't have to worry about the direction of the axis of rotation relative to the direction of gravity. Space is isotropic.

But i can't figure out how the velocity of water particle will affect the shape of the bubble ...

In weightlessness, if the cylinder is not rotated, the bubble will be spherical.
Question 1: Will the bubble still be spherical when the cylinder starts rotating in weightlessness? Why or why not?
Question 2: If the bubble is at some arbitrary point (r, θ, z) at the moment the cylinder starts rotating, will it stay there? If yes, what will its subsequent motion be? If no, why not?

 

[Raihan amin]

Question 2: If the bubble is at some arbitrary point (r, θ, z) at the moment the cylinder starts rotating, will it stay there? If yes, what will its subsequent motion be? If no, why not?

As the cylinder is closed,we can consider it, along with the water,as a rigid body.Then we can say that the bubble will keep it's position fixed.

 

[Raihan amin]

And i have no idea about the shape of the bubble when the cylinder starts rotating. Please give the actual answers of your questions .

 

[Chestermiller]

What would the pressure distribution be inside the rotating container if the bubble were not present?

 

[kuruman]

And i have no idea about the shape of the bubble when the cylinder starts rotating. Please give the actual answers of your questions .

This is how it works: You ask a question, we lead you to the answer by asking intermediate questions that you must answer yourself.

As the cylinder is closed,we can consider it, along with the water,as a rigid body.Then we can say that the bubble will keep it's position fixed.

Shouldn't the rotation make a difference? What about artificial gravity?
https://en.wikipedia.org/wiki/Artificial_gravity