6. (10 points) As illustrated in the figure below, the space between two 6-inch-long concentric cylinders is filled with glycerin (viscosity = 8.5 x 10-³ lb-s / ft²). The inner cylinder has a radius of 3in. and the gap width between cylinders is 0.1 in. Determine the torque (in units of ft-lb) required to rotate the inner cylinder at 180 revolutions/min. The outer cylinder is fixed. Assume the velocity profile in the gap to be linear and ignore viscous forces from the bottom of the cylinder ("end effects").

Fig: 1

Fig: 2