A fluid flows axially in the annular region between two concentric pipes with radii R1 and R2 > R1, respectively. Assume the flow is steady, incompressible, axisymmetric, fully-developed, and has no swirl. Also neglect all body forces.
(a) Write out the governing equations in cylindrical polar coordinate form and simplify for the above assumptions.
(b) Write down all applicable boundary conditions.
(c) Integrate the resulting equations to obtain a velocity prole for the fluid in the annular region, uz(r). Do not try to determine the constants of integration.