A two-dimensional fluid element of dimensions dx and dy translates and distorts as shown in Fig. P469

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A two-dimensional fluid element of dimensions dx and dy translates and distorts as shown in Fig. P4–69 during the infinitesimal time period dt = t2 – t1. The velocity components at point P at the initial time are u and ν in the x- and y-directions, respectively. Show that the magnitude of the rate of rotation (angular velocity) about point P in the xy-plane is

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