Why does a bolt move up/down when equal pressure acts on equal areas at different radii?

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Gh778
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With a standard bolt and nut. Create 2 areas, red and green, red surface = green surface. Green surface is closer to the center than red surface. Red surface is between up surface of bolt and bot surface of nut. Green surface is between down surface of bolt and top surface of nut. We put the same pressure from fluid in green and red volumes. Like surfaces are equal the bolt can move up or down without need energy. The nut turn only and the bolt move up/down only. Like green surface is closer to the center, the torque on the nut is bigger with red surface. The outside pressure is lower than pressure in red/green volumes. Like this it seems the nut turn with a torque, where is the problem ?
 

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Hi Gh778,

It seems your problem is not solved yet. I don't think its that complicated but you jump from one example to another one.
Another thing is that you are not satisfied with proofs based on equilibrium. For example if a chair is placed on a flat surface, and it is not moving, due to equilibrium, the total reaction forces from the surface on the chair has no x and y component , but you want to calculate the forces on each leg ( the legs have some angle rather than 90 degree with the surface) and prove that the total x and y components are zero.
 
Yes, sorry I change and I don't explain all I think :( I thought with square thread, you're remind ? It's not like the drawing show; With square thread we have calculate the torque increase with the radius not like a circular thread where the torque is the same with different radius. Imagine the bolt move up/down, the up force can be equal to the down force. The nut has a torque due to the difference of radius and when it turn it give energy. Where is the problem in this case ?
 
The force is canceled by the reaction from the nut thread because the bolt thread is not free to move alone the force direction. All the force due to pressure is normal to the surface and the the bolt thread can't move in that direction, means ALL the force is cancelled. Then what remains to cause a net torque?
 
The slope is different that's why the nut don't turn with torque I think.
 
Even with zero pressure on one of the surfaces, the net torque is zero.
 
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