1. Membrane filtration modules are often configured as bundles of hollow fibers to cause the filtrate to pass outward through the fiber wall. Let us model the flow through one fiber by considering a cylindrical tube of radius R and length L. The mean axial velocity at the tube inlet is U. The radial fluid velocity at the tube wall is Vw. To make the problem more interesting, assume that the tube is also rotating with an angular speed 2. The objective is to determine the velocities and pressure gradient in the tube. Ignore entrance/exit effects, and assume R L. Neglect gravity. c) Obtain an expression for V2. Your answer may have a pressure gradient term. d) Derive an expression for the pressure gradient in terms of known parameters. U Vw -OP/az U