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Chapt10 - The Lehigh River White Haven Pennsylvania Open...

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658 The Lehigh River, White Haven, Pennsylvania. Open channel flows are everywhere, often rough and turbulent, as in this photo. They are analyzed by the methods of the present chapter. (Courtesy of Dr. E. R. Degginger/Color-Pic Inc.)
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10.1 Introduction Motivation. The duct flows of Chap. 6 were driven by a pressure difference between the ends of the duct. Such channels are closed and full of fluid, either gas or liquid. By contrast, an open-channel flow is liquid only and is not full; i.e., there is always a free surface exposed to ambient pressure. The basic balance of forces is between grav- ity (fluid weight) and friction. Practical open-channel problems almost always concern water as the relevant fluid. The flow is generally turbulent, due to its large scale and small kinematic viscosity, and is three-dimensional, sometimes unsteady, and often surprisingly complex due to geometric effects. This chapter presents some simple engineering theories and corre- lations for steady flow in straight channels of simple geometry. Many of the concepts from steady duct flow—hydraulic diameter, friction factor, head losses—apply also to open channels. Simply stated, open-channel flow is the flow of a liquid in a conduit with a free sur- face. There are many practical examples, both artificial (flumes, spillways, canals, weirs, drainage ditches, culverts) and natural (streams, rivers, estuaries, floodplains). This chapter introduces the elementary analysis of such flows, which are dominated by the effects of gravity. The presence of the free surface, which is essentially at atmospheric pressure, both helps and hurts the analysis. It helps because the pressure can be taken constant along the free surface, which therefore is equivalent to the hydraulic grade line (HGL) of the flow. Unlike flow in closed ducts, the pressure gradient is not a direct factor in open- channel flow, where the balance of forces is confined to gravity and friction. 1 But the free surface complicates the analysis because its shape is a priori unknown: The depth profile changes with conditions and must be computed as part of the problem, espe- cially in unsteady problems involving wave motion. Before proceeding, we remark, as usual, that whole books have been written on open-channel hydraulics [1 to 4]. There are also specialized texts devoted to wave mo- tion [5 to 7] and to engineering aspects of coastal free-surface flows [8, 9]. This chap- ter is only an introduction to broader and more detailed treatments. Chapter 10 Open-Channel Flow 1 Surface tension is rarely important because open channels are normally quite large and have a very large Weber number. 659
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The One-Dimensional Approximation An open channel always has two sides and a bottom, where the flow satisfies the no- slip condition. Therefore even a straight channel has a three-dimensional velocity dis- tribution. Some measurements of straight-channel velocity contours are shown in Fig.
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