Four prototypical flow fields are expressed below in terms of Cartesian coordinates. In these expressions, y is a constant. i) Planar elongation: v= yxe - Yye, +0e. ii) Uniaxial extension: v = 2pxe - Yy e - Ye, iii) Biaxial extension: 1 = Yxe + Yy e - 2Yze iv) Pure rotation: v = Yye - yxe, +0e For each of these flows, determine: a) the rate of strain tensor e = = [Vv + Vy]] and b) the deviatoric stress tensor ( = = [Vv - Vv ]. Based on your answers to part (a), determine: c) whether the flow is incompressible (i.e., is V . v = 0?) d) whether the flow is irrotational. (i.e., is V X v = 0?)