A molten polymer is being extruded from an annular die in the form of a tube of circular cross section. This is how plumbing tubes are extruded through a profile-extruded die. The driving force for such motion is a pressure differential P across the die of length L. The die has an outer radius R1 and inner radius R2. The temperature of the polymer is T0. (a) Set up momentum balance equations for this flow in an appropriate coordinate system assuming the fluid to be a shear-thinning liquid with consistency m and power-law index n. List all other assumptions. (b) Specify the boundary conditions for solution of the velocity field. (c) Search published literature on this flow and study the papers that you are able to find. List the references to these papers in your HW report. (d) Draw sketches of velocity profile in the die gap as function of power-law index. For this, you can take help from published work. Does the velocity profile depend on the value of consistency? Explain your answer. (d) Answer the following questions qualitatively: Which of the two liquids with the same consistency, but n=0.2 and n=0.6 will need more pressure drop? Why?