A Newtonian fluid is confined in the annular space between a solid inner cylinder (radius r1) and the inner wall of a pipe (radius r2). The inner cylinder is stationary, but the outer pipe is moving upward at a velocity v2. The pressure is atmospheric on both ends of the pipe. Required:
a. Simplify the Navier Stokes Equations to describe laminar flow of the fluid in the annular space. State and justify all simplifying assumptions.
b. Write appropriate boundary conditions that could be used to integrate your result from Part A to obtain a laminar flow velocity profile of the fluid between r1 and r2.
c. Integrate your result from Part A to get an equation for velocity in terms of r and two integration constants C1 and C2. You do not need to evaluate C1 and C2.