Calculations for move in a volume in gas

[lba]

I would like to calculate the energy need for move in the black volume in gas (move in from r2 to r1), when gas is under rotating movement. The black volume turn at the same speed than gas. The weight of black volume is considered like 0. Like rotating create centripetal force, the pressure at external circle is more important than at internal, so it's not easy. Is it possible to calculate function of Gas, T, P, r1, r2, h, p, W and how can I do ? Consider "torus" like a square section and close.

At first, my idea is to say the temperature of gas don't change because gas rotating, so if the temperature don't change it's like put volume in gas without rotating but I'm not sure, could you help me ?

 

[mfb]

If h is small compared to r1 and r2, you can neglect the rotation (and the compression due to the reduced volume) - it will lead to different pressures inside+outside, but the average pressure is the same unless you heat your gas. The approximation is better if the black thing is shaped like a part of a circular sector.

 

[lba]

Yes take a part of circular sector

If h is small compared to r1 and r2, you can neglect the rotation

This even W is very high ? Could you explain a little more ? H can be greater if it's a part of circular sector ?

 

[mfb]

If the black thing is a part of a circular sector, it will remove some fixed fraction of the volume - and that fraction is the same for all distances to the center.
If h is small compared to r1 and r2, you won't compress the gas much, therefore the required energy is just the pressure, integrated over the volume you take away.

An ideal gas has a fixed pressure<->density ratio, therefore the required energy is proportional to the mass within the volume you take away - and that does not depend on the rotation.

If your black thing has a different shape, things are different.

 

[lba]

If your black thing has a different shape, things are different.

I don't understand how shape modify the result, could you explain ?

 

[mfb]

Consider a high rotation speed (gas on the outside) and a ">"-shaped object (object mainly at the inner part): Gas and object are at different places, nearly no energy required. In contrast, a "<"-shape would have to remove much gas there.

 

[lba]

1/ Ok. The result change if black volume don't turn like gas, the black volume don't "see" more temperature ?

2/ I have another question about torque with 2 different density of gas. I'm interesting about green wall only (not red). If Y>X (see drawing) the gas B will be more at external circle than gas A, so the temperature give more torque from B than from A because the radius is not the same ?

 

[mfb]

1/ Ok. The result change if black volume don't turn like gas, the black volume don't "see" more temperature ?

I don't understand that question. Are you sure you mean temperature? And how does the modified setup look like?

2/ I have another question about torque with 2 different density of gas. I'm interesting about green wall only (not red). If Y>X (see drawing) the gas B will be more at external circle than gas A, so the temperature give more torque from B than from A because the radius is not the same ?

Again: Temperature?
As shown before, for ideal gases, the integral of the pressure over the wall does not depend on the rotation.

 

[lba]

Are you sure you mean temperature? And how does the modified setup look like?

No it's not really temperature, temperature is the kinetics energy of gas. But when gas is in rotation it has more kinetics energy. An object that turn with gas see only kinetics energy from gas. When the object don't turn like gas, is it more difficult to enter the object compared with the energy when the object turn ?

For that follow: the green wall don't move in or out, it's only a wall

2/ I have another question about torque with 2 different density of gas. I'm interesting about green wall only (not red). If Y>X (see drawing) the gas B will be more at external circle than gas A, so the temperature give more torque from B than from A because the radius is not the same ?

Sorry, I did not mean temperature but pressure. The repartition of the pressure is not the same with gas A and B, true ? So, with the effect of radius the torque is not the same ? Second drawing show two integrals, they have same value but not the same repartition by radius and when calculate torque it's not the same ?

 

[mfb]

No it's not really temperature, temperature is the kinetics energy of gas.

No. Temperature of a gas is related to the unordered (!) kinetic energy, but it is not the same. And the total velocity of the gas is completely irrelevant.

When the object don't turn like gas

I don't see how this should work mechanically.

For that follow: the green wall don't move in or out, it's only a wall

I know.

The repartition of the pressure is not the same with gas A and B, true ?

Right.

So, with the effect of radius the torque is not the same ?

Probably, but the effect should be small.
The red wall receives the opposite value then.

 

[lba]

I don't see how this should work mechanically.

imagine the gas is turning in front of you (like in a wheel of bicycle for example), you move in a black volume. The gas turn and you not. Mechanically the wall must be dynamic, but it's only for compared theory energy when:

1/ gas turn, black volume turn
2/ gas turn, black volume don't turn (in this case there is frictions from gas I think)

I think the energy is the same because temperature are the same in 2 cases but I'm not sure.

 

[mfb]

How do you move a block into a turning wheel, without destroying that wheel?

2/ gas turn, black volume don't turn (in this case there is frictions from gas I think)

And complicated pressure, temperature, density and flow profiles and so on. That needs a numerical simulation.

 

[lba]

You're right, so with the animations, nothing turn except gas A, gas B and green wall (circles don't turn, no reason for that). This seems a possible mechanical movement, So like green wall recover torque while it rotate, something must be wrong in this movement ? I drawn black volume move in/out at external circle but it's more interesting to move in/out like altitude (other plane) like that this don't change the repartition of gas in volume.

 

[mfb]

Sorry, this is getting to weird for me and I have no idea what you try to find out. I think you have some underlying problem in mind, but I cannot see it in the thread.

 

[lba]

Maybe animations are not clear, I would like to see if it's possible to rotate green wall without have red wall (message #7) with this method. Temperature of gas A and B is constant, for example at 290°K regulated from external. Volume of gas A and B is constant like simulations show. So pressure is constant. I think a torque exist on green wall, this is logical. I think energy needed for remove one black volume is the same than move in it because it's the same temperature and pressure for gas A and B. Black volumes and circles don't turn. Only gas A, B and green wall turn. Maybe this need some numerical simulation but I don't understand why this mechanical movement is not possible. Like this would break 2nd law of thermodynamics I think it's not possible too.

I would like to calculate at least the torque on green wall in function of:

Density of gas A and B, pressure, temperature
speed W rd/s
R1, R2, thickness

Could you help me for that ?

 

[lba]

With this shape I don't know how torques could be cancel themselves ? Repartition are not the same and radius change in the same time.
A = Gas A of density 1
B = Gas B of density 2