in a gas absorption experiment a viscous fluid flows upward through a small circular tube and then downward in laminar flow on the outside. set up a momentum balance over a shell of thickness ar in the film,

The previous chapter provided derivations of the relationships for mass and momentum conservation—the equations of motion—in rectangular, cylindrical, and spherical coordinates.
All experimental evidence suggests that these are the most fundamental equations of fluid mechanics, and that they govern any situation involving the flow of a Newtonian fluid in principle.
Unfortunately, due to their all-encompassing nature, their solution in analytical terms is difficult or impossible to achieve except in relatively simple situations. However, it is critical to understand these "Navier-Stokes equations" for the following reasons:

1. They lead to the analytical and exact solution of some simple but important problems, as examples in this chapter will show.

2. They serve as the foundation for future research in other areas of chemical engineering.

3. Making a few realistic simplifying assumptions can often result in approximate solutions that are perfectly acceptable for many engineering purposes. Examples include the study of boundary layers, waves, lubrication, film coating of substrates, and inviscid (irrotational) flow.

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