Problem 2 (Understanding the Deformation Tensor) 30 points For each of the following questions, do Compute the strain rate tensor, Si,, and rotation tensor, Rij i. ii. Compute the rates of linear strain and shear strain. iii. Compute the vorticity of this flow. Is it irrotational? iv. (For a and b) draw a figure of the flow field. You may assume all of these flows are 2D. a. Pressure driven flow between parallel plates (Poiseuille Flow) u(x,y) = u(y²-h²), v(x, y) = 0 b. Free Vortex (Polar Coordinates) ur(r, 0) = 0, ug (r, 0) = [/r You may find the following velocity gradient in polar coordinates useful: Or 38 8- D az 3 √v= Or 38 +/ ave 3r -- 3. д c. Flow field given by the velocity components: u(x, y) = 2x-3y and v(x, y) = 3x + y d. Flow field given by the velocity components: u(x,y) =6x²y and v(x, y) = 3y² - 4xy