For the velocity field given in Problem 10.40, characterize the relative motion in this flow at an arbitrary point (x, y,z) by determining the translation, rotation, expansion, and shear deformation...

For the velocity field given in Problem 10.40, characterize the relative motion in this flow at an arbitrary point (x, y,z) by determining the translation, rotation, expansion, and shear deformation contributions to the velocity at the nearby point (x + a, y + b, z + c).

Problem 10.40

Given the velocity field u = (x²
− y²)i − 2xyj determine the velocity gradient.