A viscous fluid is contained in the space between concentric cylinders. The inner wall is fixed, and the outer wall rotates with an angular velocity \(\omega\). Fig. P6.9a Assume that the velocity distribution in the gap is linear as illustrated in Fig. P6.9b. For the small rectangular element shown in Fig. P6.9b, determine the rate of change of the right angle \(\gamma\) due to the fluid motion. Express your answer in terms of \(r_{o}, r_{i}\), and \(\omega\).

Figure P6.9

(a) (b)