Chapter 4 – Fluid Mechanics

Publisher Summary This chapter discusses how to write equations governing fluid mechanics. The equations to be written down are balance equations and constitutive equations; the former have general validity, while the latter hold only for restricted classes of materials and flow fields. Furthermore, the chapter discusses the classification of flows into laminar, turbulent, and transition in detail. Laminar flows constitute the largest class of known exact solutions of the Navier–Stokes equations. These flows are possible only for steady flows, which can be realized with parallel rectilinear streamlines. The lubrication approximation yields equations of motion, which are exactly those of a laminar flow. The other characteristic of the lubrication approximation is that, in order to neglect inertia forces, the required condition is not that the Reynolds number should be small as compared to unity, but the less restrictive condition that the product of the Reynolds number times a geometrical shape factor should be small. The various aspects of the different flows and various approximations pertaining to them such as lubrication approximation and Oseen approximation are also presented.