How to calculate sum of torque ?

[Gh778]

I would like to calculate sum of torque on object composed of one container of helium II liquid and one container of gas with low pressure. I know you think it's 0, but I would like to be sure (I think it's not 0, but it's only my intuition). It's not a theoretical problem, so I take in account different densities in fluid, this is for me the heart of the problem. Could you help me to start the problem ? I can resolve integrals but I don't know how to start. Friction of helium liquid is very low and the torque must be at 0 like Newton said, friction or not. In standard, temperature add statistically 0 force, I think it's the same in this study. NB: if system if put on Earth, gravity is perpendicular to the screen. Consider gravity from Earth like perfect.

I would like to take in account gravity and pressure but only with the law of attraction: a molecule attract a molecule with the law function of 1/d². I would like to compute all these forces to be sure there is no torque on the system.

Images:

az1 : the system is composed of one disk full of helium II liquid, inside it there is an object composed of one container of helium liquid and one container of gas under low pressure. Container of gas or container of helium liquid is part of torus with square section. Red lines are there for show containers are fixed together and the object is not deformable. The object can only turn around black disk. The disk of helium liquid is fixed, it can't move.

az3: the system after turn a lot, just for understand the rotation

az2: forces I would like to take in account, molecules of helium attract molecules of helium through the container of helium. This give a torque in one direction, an like densities are differents this torque can't be canceled by another surface. But I think it's not the only problem, for me the lack of helium don't attract container of helium and don't attract external helium, these forces must be equal but angles of lack of attraction are not the same for the container of helium and for the outside helium of the container of helium.

I hope someone can help me to start the problem. I'm starting to compute with a program but in fact the time is too long. With mathematical equations this can be resolved faster ? It's possible to resume the height of disk of helium of thickness 1 molecule ?

 

[Simon Bridge]

I would like to calculate sum of torque on object composed of one container of helium II liquid and one container of gas with low pressure. I know you think it's 0, but I would like to be sure (I think it's not 0, but it's only my intuition). It's not a theoretical problem, so I take in account different densities in fluid, this is for me the heart of the problem.

We've been here before ...

There is no net force on either regeon so why would there be any torques?
Your second diagram asserts that there are more molecules on one end than the other and that they have some special attraction to each other. How do these things happen?

i.e.
why would there be more molecules at one end than the other?
what is the mechanism for the helium inside the container attracting the helium outside?

 

[Gh778]

The same, I understood my error. Thanks