I do not readily see a way for you to easily calculate (or estimate) the torque. You will probably have to measure it. I would attach the brush to a digital torque wrench, insert the brush into the tube, and then rotate the tube along its long axis. I initially thought you would be rotating the brush instead of the tube but that won't work unless the rotational speed was very slow and you could manually rotate the brush/torque wrench setup inside the tube. FYI, I expect the torque to be dependent on rotational speed.

Gordon L Warren Thank you very much for your answer. I want to rotate the brush inside the tube because i am making a cleaning tool. For that i need to calculate the minimum torque to rotate the brush.

Lakhamanbhai Odedara But you will get the same torque if the brush is stationary and the tube is rotating. Find a long socket that will fit on your torque wrench and embed the brush in that socket using epoxy (or similar) glue. Mount the tube on a drill press or lathe. Put the brush of the brush/torque wrench assembly in the tube and turn the drill press/lathe on. You will probably want to measure torque at several different rotational speeds.

Gordon L Warren Thank you very much for the answer. I have one last question regarding this problem. I want to know if any why to find the torue theoritically. By theoriticaly means with formula in this case.

Lakhamanbhai Odedara No, I see no way to calculate the torque. The resistance to turning the tube on the brush will be very dependent on the dimensions of the tube and brush as well as the properties of the the metal brush.

Dear @Gordon L Warren thank you for explaination. I am going to measure the torque experimentally with spring loaded lever. As explained i will keep the brush stationary and rotate the pipe.