In the system below for measuring fluid viscosity, the inner cylindrical core is stationary; the outer cylindrical shell is rotated at a constant angular velocity of 900 revolution per minute; and the required torque is measured. The outer cylindrical shell has a radius of r =2 cm; the outer cylindrical shell and inner cylindrical core are separated by a distance of 0.02mm; and the two cylinders have a length of L = 2 cm. You perform a test with the following results: at a temperature of 20 "C, the torque is 0.38 Nm. What is the fluid viscosity at 20 "C assuming the velocity distribution in the fluid is linear and the effect of gravity is negligible?
Please:
(1). Derive an equation for viscosity of the fluid in terms of torque, angular velocity, and other system parameters.
(2). Determine of the viscosity of the fluid with the parameters given.