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1、Reading Material 12Principles of Momentum transfer1.IntroductionThe flow and behavior of fluid is important in many of the unit operations in process engineering. A fluid may be defined as a substance that does not permanently resist distortion and, hence, will change its shape. In this text gases,
2、liquids, and vapors are considered to have the characteristics of fluids and to obey many of the same laws.2. Fluid Flow The principles of the statics of fluids are almost an exact science. On the other hand, the principles of the motions of fluids are quite complex. The basic relations describing t
3、he motions of a fluid are the equations for the overall balances of mass, energy, and momentum, which will be covered in the following sections.The study of momentum transfer, or fluids mechanics as it is often called, can be divided into tow branches: fluid statics, or fluid at rest, and fluid dyna
4、mics, or fluids in motion. In other sections we treat fluid statics; in the remaining sections, fluid dynamics. Since in fluid dynamics momentum is being transferred, the term “momentum transfer” or “transfer” is usually used.In momentum transfer we treat the fluid as a continuous distribution of ma
5、tter or as a “continuum”. This treatment as a continuum is valid when the smallest volume of fluid contains a large enough number of molecules so that a statistical average is meaningful and the macroscopic properties of the fluid such as density, pressure, and so on, vary smoothly or continuously f
6、rom point to point.Like all physical matter, a fluid is composed of an extremely large number of molecules per unit volume. A theory such as the kinetic theory of gases or statistical mechanics treats the motions of molecules in terms of statistical groups and not in terms of individual molecules. I
7、n engineering we are mainly concerned with the bulk or macroscopic behavior of a fluid rather than with the individual molecular or microscopic behavior.In the process industries, many of the materials are in fluid form and must be stored, handled, pumped, and processed, so it is necessary that we b
8、ecome familiar with the principles that govern the flow of fluids and also with the equipment used. Typical fluids encountered include water, air, CO2, oil, slurries, and thick syrups.If a fluid is inappreciably affected by change in pressure, it is said to be incompressible. Most liquids are incomp
9、ressible. Gases are considered to be compressible fluids. However, if gases are subjected to small percentage changes in pressure and temperature, their density changes will be small and they can be considered to be incompressible. 3. Laminar and Turbulent Flow The type of flow occurring in a fluid
10、in a channel is important in fluid dynamics problems. When fluids move through a closed channel of any cross section, either of tow distinct types of flow can be observed according to the conditions present. These two types of flow can be commonly seen in a flowing open stream or river. When the vel
11、ocity of flow is slow, the flow patterns are smooth. However, when the velocity is quite high, an unstable pattern is observed in which eddies or small packets of fluid particles are present moving in all directions and at all angles to the normal line of flow. The first type of flow at low velociti
12、es where the layers of fluid seem to slide by one another without eddies or swirls being present is called laminar flow and Newtons law of viscosity holds. The second type of flow at higher velocities where eddies are present giving the fluid a fluctuating nature is called turbulent flow.The existen
13、ce of laminar and turbulent flow is most easily visualized by the experiments of Reynolds. Water was allowed to flow at steady state through a transparent pipe with the flow rate controlled by a valve at the end of the pipe. A fine steady stream of dye-colored water was introduced from a fine jet as
14、 shown and its flow pattern observed. At low rates of water flow, the dye pattern was regular and formed a single line or stream similar to a thread. There was no lateral of the fluid, and it flowed in streamlines down the tube. By putting in additional jets at other points in the pipe cross section
15、, it was shown that there was no mixing in any parts of the tube and the fluid flowed in straight parallel lines. This type of flow is called laminar or viscous flow.As the velocity was increased, it was found that at a define velocity the thread of dye become dispersed and the pattern was very erra
16、tic. This type of flow is known as turbulent flow. The velocity at which the flow changes is known as the critical velocity.4. Reynolds NumberStudies have shown that the transition from laminar to turbulent flow in tubes is not only a function of velocity but also of density and viscosity of the fluid and the tube diameter. These variables are combined into the Reynolds number, which is dimensionless. R=Where Re is the Reynolds number, D the diameter in m
