Hi,
At university I had a course where I learned to compute the pressure raise and pressure drop (on the dies) on one extruder along the screw. We were using transport equations to compute the flow in the screw. The equations were divided in three steps, one equation for solids transport, other for solids + melt, and a final one for melt. The screw was considered to be flat.
The screw speed was given by us.
I believe that if you take those equations you will be able to calculate the torque that needs to be applied to make the screw move.
I don't have my notes, but I remember the name of two books that I used on this course and may be helpful for you:
Principles of Polymer Processing by Tadmor & Gogos
Polymer Extrusion by Chris Rauwendaal
To calculate the torque that you have on the drive you will need all the data from the drive - as mentioned.
Hope this can help,
Gil