i would like the working out using the SHELL BALANCE method.

3. Flow through Annular Die Consider a die that forms a tube of polymer (other shapes being sheets and filaments). In the die of length D shown in Fig. 3, a pressure difference p2 - p3 causes a liquid of viscosity u to flow steadily from left to right in the annular area between two fixed concentric cylinders. The inner cylinder is solid, whereas the outer one is hollow; their radii are rl and r2, respectively. The problem, which could occur in the extrusion of plastic tubes, is to find the velocity profile in the annular space and the total volumetric flow rate Q. Note that cylindrical coordinates are now involved. P2 Outer wall Velocity profile P3 Inlet Exit Axis of symmetry Fixed inner cylinder Fluid D Figure 3. Geometry for flow through an annular die