Consider again the viscometric flow of Example 5.7. Evaluate the average rate of rotation of a pair of perpendicular line segments oriented at \(\pm 45^{\circ}\) from the \(x\) axis. Show that this is the same as in the example.

Data From Example 5.7

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Example 5.7 ROTATION IN VISCOMETRIC FLOW A viscometric flow in the narrow gap between large parallel plates is shown. The velocity field in the narrow gap is given by V = U(y/h)i, where U = 4 mm/s and h=4 mm. At t=0 line segments ac and bd are marked in the fluid to form a cross as shown. Evaluate the positions of the marked points at t=1.5s and sketch for comparison. Calculate the rate of angular deformation and the rate of rotation of a fluid particle in this velocity field. Comment on your results. u = U 1- U b (2,3) a (1,2) 2 c(3,2) Lines marked 'd (2,1) in fluid at t=0 0 0 1 2 3