How does angular velocity affect the density of water in a rotating container?

[bartekac]

Hi,

I was recently thinking about a problem which I have no idea how to solve.
A full water container with volume V is hanged on a rope with length L (mass of the rope is negligible). It then starts to revolute around the point where the rope is hooked (circular motion, circle with radius L) with angular velocity ω.
Express the water density ρ as a function of V, L, and ω.

Thanks in advance for any help.

 

[Chestermiller]

Is this a homework problem?

Chet

 

[bartekac]

No, it is not.
I was just concerned that I have actually no idea how to approach it.

 

[Chestermiller]

No, it is not.
I was just concerned that I have actually no idea how to approach it.

OK. Tell us in words what you think will be happening.

Chet

 

[bartekac]

Ok.
I suppose the water density will increase as a result of centrifugal force causing the molecules to move closer to one another.

 

[mrspeedybob]

Water, under a wide variety of conditions, can be considered a non-compressible fluid. If your experiment is to be conducted in this range of conditions then p would simply be the density of water (about 1 gram per cubic centimeter). If your experiment is under more extreme conditions, it would be helpful to know what those conditions are.

 

[bartekac]

In general, what interests me here is how to approach the problem of calculating the compression of a fluid in the described situation.
Can water still be considered non-compressible if the container was, for instance, moving with a linear velocity L\omega>\frac{1}{4}c?

 

[Chestermiller]

Water is slightly compressible. The density of a fluid is related to the pressure on the fluid by
$$\frac{1}{\rho}\frac{d\rho}{dp}=β$$
where β is a physical property of known as the compressibility. You can look up the compressibility of water on Google for room temperature. So, if you can calculate how the pressure is varying spatially as a result of how you are moving the bucket, you can determine how the density is varying. You can determine the pressure variation by applying Newton's second law to the fluid locally.

In any event, the change in density will typically be very small even in a centrifuge.

Chet