Chapt06 - Steam pipe bridge in a geothermal power plant...

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Steam pipe bridge in a geothermal power plant. Pipe flows are everywhere, often occurring in groups or networks. They are designed using the principles outlined in this chapter. (Courtesy of Dr. E. R. Degginger/Color-Pic Inc.) 324
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6.1 Reynolds-Number Regimes Motivation. This chapter is completely devoted to an important practical fluids engi- neering problem: flow in ducts with various velocities, various fluids, and various duct shapes. Piping systems are encountered in almost every engineering design and thus have been studied extensively. There is a small amount of theory plus a large amount of experimentation. The basic piping problem is this: Given the pipe geometry and its added compo- nents (such as fittings, valves, bends, and diffusers) plus the desired flow rate and fluid properties, what pressure drop is needed to drive the flow? Of course, it may be stated in alternate form: Given the pressure drop available from a pump, what flow rate will ensue? The correlations discussed in this chapter are adequate to solve most such pip- ing problems. Now that we have derived and studied the basic flow equations in Chap. 4, you would think that we could just whip off myriad beautiful solutions illustrating the full range of fluid behavior, of course expressing all these educational results in dimensionless form, using our new tool from Chap. 5, dimensional analysis. The fact of the matter is that no general analysis of fluid motion yet exists. There are several dozen known particular solutions, there are some rather specific digital- computer solutions, and there are a great many experimental data. There is a lot of the- ory available if we neglect such important effects as viscosity and compressibility (Chap. 8), but there is no general theory and there may never be. The reason is that a profound and vexing change in fluid behavior occurs at moderate Reynolds numbers. The flow ceases being smooth and steady ( laminar ) and becomes fluctuating and agi- tated ( turbulent ). The changeover is called transition to turbulence. In Fig. 5.3 a we saw that transition on the cylinder and sphere occurred at about Re 3 10 5 , where the sharp drop in the drag coefficient appeared. Transition depends upon many effects, e.g., wall roughness (Fig. 5.3 b ) or fluctuations in the inlet stream, but the primary parame- ter is the Reynolds number. There are a great many data on transition but only a small amount of theory [1 to 3]. Turbulence can be detected from a measurement by a small, sensitive instrument such as a hot-wire anemometer (Fig. 6.29 e ) or a piezoelectric pressure transducer. The 325 Chapter 6 Viscous Flow in Ducts
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Fig. 6.1 The three regimes of vis- cous flow: ( a ) laminar flow at low Re; ( b ) transition at intermediate Re; ( c ) turbulent flow at high Re. flow will appear steady on average but will reveal rapid, random fluctuations if turbu- lence is present, as sketched in Fig. 6.1. If the flow is laminar, there may be occasional natural disturbances which damp out quickly (Fig. 6.1 a ). If transition is occurring, there will be sharp bursts of turbulent fluctuation (Fig. 6.1 b
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