A compact device that may be used to measure viscosity and other flow properties of fluids is the parallel-plate torsional rheometer (Figure XXXXXXXXXXIn this device, the gap between two circular...

A compact device that may be used to measure viscosity and other flow properties of fluids is the parallel-plate torsional rheometer (Figure 6.18). In this device, the gap between two circular disks is filled with fluid and one of the disks is turned. The design is such that the velocity field in the gap is given by:

The viscosity is related to the torque required to turn the disk. For a Newtonian fluid in such an apparatus, how is the viscosity related to the total torque to turn the top disk?