3 - Description of Fluid Motion

Summary

This chapter introduces the description of fluid motion, that is, the fluid kinematics. At first, the Lagrangian and Eulerian method is compared to emphasize that most problems in fluid mechanics is more suitable for Eulerian method. Secondly, the concepts of pathlines and streamlines are introduced. Next, Acceleration equation and substantial derivative are derived in Eulerian coordinates and their physical significance is discussed in depth and in examples. Reynolds transport theorem is then introduced and compared with substantial derivative to demonstrate that they are the same relation in integral and differential form respectively. Deformation of a finite fluid element is discussed in the next. Linear deformation, rotation, angular deformation equations are derived individually with equations and illustrations. These knowledges are the key to derive the differential equations of a flow, which will be introduced in chapter 4.