Microfluidics: Modeling, Mechanics and Mathematics

Chapter 14

The Circular Flow Tube

14.1 Introduction

In this section, we will derive the fluid mechanics of the circular flow tube. Flow tubes as control volumes were introduced in section 10.1.4. They represent a very simple type of control volume and can be used whenever a fluid flow is parallel. The circular flow tube is the simplest case of a flow tube. It exploits the fact that a cylindrical coordinate, although being a three-dimensional object, can be treated mathematically as a two-dimensional problem if the mechanics are derived in cylindrical coordinates (see section 7). In general, the cylindrical coordinate system uses three axes: ${\overrightarrow{e}}_r$ (radius), ${\overrightarrow{e}}_{\phi }$ (rotation around ${\overrightarrow{e}}_z$, azimuthal angle), and ${\overrightarrow{e}}_z$. However, in cylindrical flow tubes, ...