Fig. P6.13 Section of a Couette viscometer. 13. Torque in a Couette viscometer-M. Fig. P6.13 shows the horizontal cross section of a concentric cylinder or "Couette" viscometer, which is an apparatus for determining the viscosity of the fluid that is placed between the two vertical cylinders. The inner and outer cylinders have radii of r1 and r2, respectively. If the inner cylinder is rotated with a steady angular velocity , and the outer cylinder is stationary, derive an expression for v (the velocity component) as a function of radial location r. If, further, the torque required to rotate the inner cylinder is found to be T per unit length of the cylinder, derive an expression whereby the unknown viscosity can be determined, in terms of T,,r1, and r2. Hint: You will need to consider one of the shear stresses given in Table 5.8