Bài tập thủy lực - chương 4

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Bài tập thủy lực - chương 47708d_c04_160-203 7/23/01 9:51 AM Page 160 A vortex ring: The complex, three-dimensional structure of a smoke ring is indicated in this cross-sectional view. 1Smoke in air.2 1Photograph courtesy of R. H. Magarvey and C. S. MacLatchy, Ref. 4.27708d_c04_160-203 7/23/01 9:51 AM Page 161 4 Fluid Kinematics In the previous three chapters we have defined some basic properties of fluids and have con- sidered various situations involving fluids that are either at rest or are moving in a rather el- ementary manner. In general, fluids have a well-known tendency to move or flow. It is very difficult to “tie down” a fluid and restrain it from moving. The slightest of shear stresses will cause the fluid to move. Similarly, an appropriate imbalance of normal stresses 1pressure2 will cause fluid motion. In this chapter we will discuss various aspects of fluid motion without being concerned with the actual forces necessary to produce the motion. That is, we will consider the kine- Kinematics involves matics of the motion—the velocity and acceleration of the fluid, and the description and vi- position, velocity, sualization of its motion. The analysis of the specific forces necessary to produce the mo- and acceleration, tion 1the dynamics of the motion2 will be discussed in detail in the following chapters. A wide not force. variety of useful information can be gained from a thorough understanding of fluid kine- matics. Such an understanding of how to describe and observe fluid motion is an essential step to the complete understanding of fluid dynamics. We have all observed fascinating fluid motions like those associated with the smoke emerging from a chimney or the flow of the atmosphere as indicated by the motion of clouds. The motion of waves on a lake or the mixing of paint in a bucket provide other common, al- though quite different, examples of flow visualization. Considerable insight into these fluid motions can be gained by considering the kinematics of such flows without being concerned with the specific force that drives them. 4.1 The Velocity Field In general, fluids flow. That is, there is a net motion of molecules from one point in space to another point as a function of time. As is discussed in Chapter 1, a typical portion of fluid con- tains so many molecules that it becomes totally unrealistic 1except in special cases2 for us to at- tempt to account for the motion of individual molecules. Rather, we employ the continuum hy- pothesis and consider fluids to be made up of fluid particles that interact with each other and 1617708d_c04_160-203 8/10/01 12:53 AM Page 162 162 I Chapter 4 / Fluid Kinematics z Particle A at Particle path time t + δ t Particle A at time t rA(t) rA(t + δ t) y I FIGURE 4.1 Particle location in terms of its position ...