Consider fully developed Couette flow—flow between two infinite parallel plates separated by distance h, with the top plate moving and the bottom plate stationary as illustrated in Fig. P4–79. The flow is steady, incompressible, and two-dimensional in the xy-plane. The velocity field is given by

Is this flow rotational or irrotational? If it is rotational, calculate the vorticity component in the z-direction. Do fluid particles in this flow rotate clockwise or counterclockwise?

FIGURE P4–79

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V = (u, v) = V² i + oj h