Chapter 1, Problem 1.56P

The device in Fig. P1.56 is called a cone-plate viscometer [29]. The angle of the cone is very small, so that sin $\theta \approx \theta$, and the gap is filled with the test liquid. The torque M to rotate the cone at a rate $\Omega$ is measured. Assuming a linear velocity profile in the fluid film, derive an expression for fluid viscosity $\mu$ as a function of (M, R, $\Omega$ , $\theta$).