Bài tập thủy lực- chương 3

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Bài tập thủy lực- chương 37708d_c03_100 8/10/01 3:01 PM Page 100 mac120 mac120:1st shift: Flow past a blunt body: On any object placed in a moving fluid there is a stagnation point on the front of the object where the velocity is zero. This location has a relatively large pressure and divides the flow field into two portions—one flowing over the body, and one flowing under the body. 1Dye in water.2 1Photograph by B. R. Munson.27708d_c03_101 8/10/01 3:01 PM Page 101 mac120 mac120:1st shift: 3 Elementary Fluid Dynamics—The Bernoulli Equation As was discussed in the previous chapter, there are many situations involving fluids in which the fluid can be considered as stationary. In general, however, the use of fluids involves mo- tion of some type. In fact, a dictionary definition of the word “fluid” is “free to change in form.” In this chapter we investigate some typical fluid motions 1fluid dynamics2 in an ele- mentary way. To understand the interesting phenomena associated with fluid motion, one must con- sider the fundamental laws that govern the motion of fluid particles. Such considerations in- clude the concepts of force and acceleration. We will discuss in some detail the use of New- ton’s second law 1 F ma 2 as it is applied to fluid particle motion that is “ideal” in some sense. We will obtain the celebrated Bernoulli equation and apply it to various flows. Al- though this equation is one of the oldest in fluid mechanics and the assumptions involved in its derivation are numerous, it can be effectively used to predict and analyze a variety of flow situations. However, if the equation is applied without proper respect for its restrictions, se- rious errors can arise. Indeed, the Bernoulli equation is appropriately called “the most used The Bernoulli and the most abused equation in fluid mechanics.” equation may be A thorough understanding of the elementary approach to fluid dynamics involved in the most used and this chapter will be useful on its own. It also provides a good foundation for the material in abused equation in fluid mechanics. the following chapters where some of the present restrictions are removed and “more nearly exact” results are presented. 3.1 Newton’s Second Law As a fluid particle moves from one location to another, it usually experiences an acceleration or deceleration. According to Newton’s second law of motion, the net force acting on the fluid particle under consideration must equal its mass times its acceleration, F ma 1017708d_c03_102 8/10/01 3:02 PM Page 102 mac120 mac120:1st shift: 102 I Chapter 3 / Elementary Fluid Dynamics—The Bernoulli Equation In this chapter we consider the motion of inviscid fluids. That is, the fluid is assumed to have zero viscosity. If the viscosity is zero, then the thermal conductivity of the fluid is also zero and there can be no heat transfer 1except by radiation2. In practice there are no inviscid fluids, since every fluid supports shear stresses when it is subjected to a rate of strain displacement. For many flow situations the viscous effects are relatively small compared with other effects. As a first approximation for such cases it is often possible to ignore viscous effects. For example, often the viscous forces developed in flowing water may be several orders of magnitude smaller than forces due to other influ- ences, such as gravity or pressure differences. For other water flow situations, however, the viscous effects may be the dominant ones. Similarly, the viscous effects associated with the flow of a gas are often negligible, although in some circumstances they are very important. We assume that the fluid motion is governed by pressure and gravity forces only and Inviscid fluid flow examine Newton’s second law as it applies to a fluid particle in the form: in governed by 1 Net pressure force on a particle 2 1 net gravity force on particle 2 pressure and grav- ity forces. 1 particle mass 2 1 particle acceleration 2 The results of the interaction ...