Fluid Mechanics for Chemical Engineers with Microfluidics and CFD, Second Edition

Chapter 5. Differential Equations of Fluid Mechanics

5.1. Introduction to Vector Analysis

The various quantities used in fluid mechanics may be subdivided into the categories of scalars, vectors, and tensors. At any point in space and time, a scalar needs only a single number to represent it, examples being temperature, volume, and density. A vector, however, needs for its description both a magnitude and a direction, examples being force, velocity, and momentum; for example, the gravitational force on one kilogram is g newtons, vertically downward. A tensor is more complicated, and its discussion will be postponed until the shear-stress tensor is introduced in Section 5.7. Appendix C gives details of a few important vector and tensor operations ...