Problem 2: Leaming Outcomes Used in This Problem: 1. Define a shell volume 2. Perform microscopic momentum balances 3. Apply relevant boundary conditions In a continuous coating process shown below, a Newtouian and incompressible liquid is extruded through a slot into a die outo a solid sheet moving at speed U. The pressure at the slot exit is PI and the gap thickness between sheet and die is h. There is forward flow in a region above length L1. Liquid is also flowing in a region above length L2, but there is zero net flow. It may be assumed that surface tension is negligible. A mass balance has already been conducted and demonstrates that x-directed fluid velocity is not a function of x. The width of the die coming in and out of the page is W. You may assume steady state. a) Using a shell balance, derive the following differential equation above the length L1: dy2d2vx=L1P1P0 b) What are the botmdary conditions for the region above length L4 ? c) Solve the differential equation for vs for the region above length L. Show that the equation is the following: yvn=2L1v(p1P1)k2[hyh2y2]+[1hy]