Centrifugal forces + pressure and CG

Gh778

Take half torus with solid part of density 1, other half torus with liquid of density 1. The torus turn at W rd/s enough for maintain liquid at external circle. Now, for 0 to 180° we accelerate torus, this increase forces (blue in drawing) from pressure of water and from 180° to 360° we deccelerate torus. Rotationnal speed change from W to W+w to W. It's like torus change the CG without external forces. I thought solid give pressure too but I can imagine 2 liquids with different density, it's the same. I have some questions:

1/ water don't give pressure so no force exist ?
2/ solid give same pressure ?
3/ when we rotate the forces from rotation, this cancel pressure forces ?

Edit: I add another drawing for show different positions

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Gh778

Maybe my questions are not precise enough ?
When I drawn solid in black, it's possible to imagine it maintain from center of circle with solid like this no pressure can appear from solid (imagine a lot of smal ropes for maintain all part of solid). So if solid don't give pressure, it is liquid that don't give pressure ?

Studiot

Does this attachment help?

There is certainly a tangential ring pressure developed in a rotating ring. In a solid it is a stress and in a liquid it is pressure. Of course these are equal in your ring because the densities are equal. For unequal densities you would have to relocate the centre of mass.

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AlephZero

I don't understand exactly what you are doing here, but one difference between the solid and liquid parts is that there must be a container that holds the liquid, and the container will apply a force to the liquid. If you ignore that fact, you will get the wrong forces and stresses.

Gh778

I'll try to understand this evening. That I can't understand: if I imagine solid half torus like small parts, if each part is attached by a rope, the pressure could be limited a lot I think ?

ok, but this force (the force the container apply) will put on support that take system ?

Chestermiller

This is actually a very complicated problem. Based on lots of experience in fluid and solid mechanics modelling, I can tell you that the best way to approach a problem like this is to start with some much simpler versions of the problem, and solve them first, and gradually add complexity until you get to the actual problem you are trying to solve. Why? First of all, if you can't solve the simpler versions of the problem, you certainly won't be able to solve the more complex problem. Secondly, you will gain understanding along the way from the solutions to the simpler problems.

In the system you describe, neither the solid nor the liquid will behave as a rigid body. Both will experience transient non-homogeneous deformations. The liquid will exhibit viscous flow that has to be accounted for, and the solid will exhibit elastic deformation that has to be accounted for. I suggest starting out with the following very simple problem:

Consider an infinitely long straight pipe containing a viscous fluid. Initially the pipe and the fluid are at rest. At time zero, the pipe is set in motion with a steady velocity V along its axis. What is the velocity and pressure distribution within the fluid as a function of time and radial position? If you can't solve this problem, you will never be able to do the torus problem.

As a second version of the problem, consider the same pipe and fluid, but this time make the imposed pipe velocity a function of time.

As a third problem, consider the case where there are rigid plugs within the pipe, and a finite length of fluid between the plugs. The plugs move with the pipe velocity.

Gh778

With W = constant, it's a complicated problem too ? or it's because W change in time ?

With W=constant, are there forces from liquid ? I think forces from solid can't be near 0 if there is a lot of parts (imagine infinite number of parts and ropes). Even if there are forces from liquid is strange because even on a round forces cancel themselves if we place this system on another object in a part of time (60° for example), this change the CG of object I think.

For change velocity, we can change the rotation of the system or place a lot of stems for help solid and liquid to gain velocity very quickly. In theory, if velocity is apply on each atom of liquid and solid, forces are centripetal forces only.

AlephZero

Compresibiitiy or elasticity doesn't have any effect on the stress field, unless you want to model this as a large displacement nonlinear problem. The body forces that cause the centripetal acceleration are known from the geometry and density, and the body forces are also the gradient of the stress tensor. The stresses are independent of the material properties, for a given set of the boundary conditions.

The boundary conditions are the key to the actual stress distrubition. For a rotating solid thin ring or cylinder with no radial constraints imposed, the main stress compoent is tension around the circumference of the ring. But a fluid can't sustain any significant tensile stress (or negative hydrostatic pressure if you prefer to call it that), so there must be some radial constraint forces (for example the fluid pressure on the solid structure that is containing it) to make the situation physically realistic.

Chestermiller

If the angular velocity is constant, then, as you indicate, then liquid and the solid can be treated as rigid, and the system will be statically determinate. However, if the angular velocity varies with time, then you have to consider the deformational mechanics of both the solid and the liquid.

Chestermiller

If W is constant, then, as AlephZero points out, the analysis is much simpler than if W varies with time. But this is not the problem that you posed.

blind light

Could any of these forces apply to the earths core?

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Gh778

1/ I would like to know if there are forces from pressure of liquid when W = constant ? AlephZero said that container would give the same force but that force come from the support of the system, right ? So the system oscillate around a point, the CG move ?

2/ If W varies with time, it's easy to change the system for accelerate/deccelerate not the support of the system but a lot of parts of solid and liquid for reduce problem from deformation I think.

@Studiot:
Where come from this tangential force ? Could you explain, I don't understand ?

@Blind light:
Do you know an effect not explain on Earth and forces can explain ?

Studiot

I don't think AZ mentioned the system support, however you did in post#5.

AZ did say

and I concur exactly.

So let us take things one step at a time.

Do you understand the idea that any rotating object will be subject to internal forces that can be resolved in two directions at right angles - radially and tangentially?

Gh778

No, I don't understand that. I see only centripetal forces. Could you explain ?

you don't understant the system or the goal of the system ? If it's the goal, it's only for study it. I know the CG can't move but I don't see that.

Studiot

Which direction do you think angular momentum acts?

Gh778

(I want to understand first when W = constant) it's tangential but I don't see how forces come from on your drawing at message #3

Studiot

We were discussing circumferential (tangential) stresses in rotating discs recently here.

http://www.physicsforums.com/showthr...light=rotation