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 shear strain rate about point P in the xy-plane is

Figure 69

Transcribed Image Text:

Line b v B dy P 77/2 dx B' Line b- Fluid element at time ₁ A P' Line a Fluid element at time t u Line a X α