A two dimensional fluid element of dimensions dx and dy translates and distorts as shown in Fig P469 during the infinitesimal time period dt t 2 t 1 The velocity components at point P at the initial time are u and in the x and y directions, respectively Show that the magnitude of the rate of rotati...

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

Question:

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