Before some time designated t=0, an incompressible, Newtonian fluid is stationary in a horizontal chamber. At t=0, a pressure is applied to the fluid to begin its flow through the chamber. After some time, the flow becomes fully-developed, but remains laminar, and we reach a steady state profile. Your assignment is to simulate and animate the transition from stationary (initial condition is for all locations) to steady-state for three different geometries using finite difference method and matlab.

Case 1: Pressure driven fluid flow between two stationary plates (both parallel to the xz plane). Let z be the direction of fluid flow for some unspecified time t. (There is another stationary plate 2 cm above the first plate.) It may be easiest to solve this problem by letting y=0 be the centerline of the fluid, and not one of the stationary plates.