The space between two $18-$in$.-$long concentric cylinders is filled with glycerin $($viscosity $=8\mathrm{.}5\backslash$times $10-31$bs$/$ft$3).$ The inner cylinder has a radius of$2$ in$.$ and the gap width between cylinders is $0\mathrm{.}1$ in$.$ Determine $($a$)$ the torque and $($b$)$ the power required to rotate the inner cylinder at $180$ rev$/$min$.$ The outer cylinder is fixed. Assume the velocity distribution in the gap to be linear.