Consider the simple shear flow described as vx = ?γ y and vy = 0, where γ? is the rate of strain

Consider the simple shear flow described as vx = ?γ y and vy = 0, where γ? is the rate of strain. Verify that the rate of strain has only shear components as shown in the text. Now consider a coordinate system that is rotated by an angle θ to the x-axis. Find the components of the vector v in this system. Then write the expression for the velocity-gradient, rate-of-strain, and vorticity tensors. Find the angle θ such that the rate of strain has only diagonal components. (Answer: θ = π/4.) This represents a case where the strain is purely elongational. Show that the vorticity tensor remains unchanged by the rotation of the coordinates.