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Ebook Fluid mechanics (edition): Part 2

(BQ) Part 2 book "Fluid mechanics" has contents: Approximate solutions of the navier–stokes equation; flow over bodies - Drag and lift; compressible flow; turbomachinery; open channel flow, property tables and charts. | cen72367_ch10.qxd 11/4/04 7:19 PM Page 471 CHAPTER 10 A P P R O X I M AT E S O L U T I O N S O F T H E N AV I E R – S T O K E S E Q U AT I O N n this chapter we look at several approximations that eliminate term(s), reducing the Navier–Stokes equation to a simplified form that is more easily solvable. Sometimes these approximations are appropriate in a whole flow field, but in most cases, they are appropriate only in certain regions of the flow field. We first consider creeping flow, where the Reynolds number is so low that the viscous terms dominate (and eliminate) the inertial terms. Following that, we look at two approximations that are appropriate in regions of flow away from walls and wakes: inviscid flow and irrotational flow (also called potential flow). In these regions, the opposite holds; i.e., inertial terms dominate viscous terms. Finally, we discuss the boundary layer approximation, in which both inertial and viscous terms remain, but some of the viscous terms are negligible. This last approximation is appropriate at very high Reynolds numbers (the opposite of creeping flow) and near walls, the opposite of potential flow. I OBJECTIVES When you finish reading this chapter, you should be able to ■ ■ ■ ■ Appreciate why approximations are necessary to solve many fluid flow problems, and know when and where such approximations are appropriate Understand the effects of the lack of inertial terms in the creeping flow approximation, including the disappearance of density from the equations Understand superposition as a method of solving potential flow problems Predict boundary layer thickness and other boundary layer properties 471 cen72367_ch10.qxd 11/4/04 7:19 PM Page 472 472 FLUID MECHANICS 10–1 “Exact” solution Full Navier–Stokes equation Analysis Solution Approximate solution Simplified Navier–Stokes equation Analysis Solution FIGURE 10–1 “Exact” solutions begin with the full Navier–Stokes equation, while approximate solutions begin with