Chapter 10

# Chapter 10 - Motion of water induced by surface waves As a...

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Unformatted text preview: Motion of water induced by surface waves: As a wave passes along the surface of the water, the water particles follow elliptical paths. There is no net motion of the water, just a periodic, cyclic trajectory 1 neutrally buoyant particles in water 2 . 1 Photograph by A. Wallet and F. Ruellan, Ref. 13, courtesy of M. C. Vasseur, Sogreah. 2 Open-channel flow involves the flow of a liquid in a channel or conduit that is not com- pletely filled. There exists a free surface between the flowing fluid 1 usually water 2 and fluid above it 1 usually the atmosphere 2 . The main driving force for such flows is the fluid weightâ€” gravity forces the fluid to flow downhill. Under steady, fully developed flow conditions, the component of the weight force in the direction of flow is balanced by the equal and oppo- site shear force between the fluid and the channel surfaces. For unsteady or nonfully devel- oped situations, the inertia of the following fluid is also important. Such flows are different from the pipe flows discussed in Chapter 8 in that there can be no pressure force driving the fluid through the channel or conduit. Any attempt to impose a pressure gradient in the flow direction is met with failure because of the negligible iner- tial and viscous effects of the gas 1 atmosphere 2 above the flowing fluid. For steady, fully de- veloped channel flow, the pressure distribution within the fluid is merely hydrostatic. Open-channel flows are essential to the world as we know it. The natural drainage of water through the numerous creek and river systems is a complex example of open-channel flow. Although the flow geometry for these systems is extremely complex, the resulting flow properties are of considerable economic, ecological, and recreational importance. Other ex- amples of open-channel flows include the flow of rainwater in the gutters of our houses; the flow in canals, drainage ditches, sewers, and gutters along roads; the flow of small rivulets and sheets of water across fields or parking lots; and the flow in the chutes of water rides in amusement parks. Clearly the character, description, and complexity of open-channel flow geometry are quite variable. The bounding geometry for flow in a sewer pipe laid on a constant slope and running half-full is much simpler than the geometry of the Mississippi River with its vari- able cross-sectional shape, bends, bottom slope variation, and character of its bounding sur- faces. Because of complexities like these, most open-channel flow results are based on cor- relations obtained from model and full-scale experiments. Additional information can be gained from various analytical and numerical efforts. 621 10 O pen-Channel Flow Open-channel flows are essential to the world as we know it. The purpose of this chapter is to investigate the concepts of open-channel flow. Be- cause of the amount and variety of material available, only a brief introduction to the topic can be presented. Further information can be obtained from the references indicated.can be presented....
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Chapter 10 - Motion of water induced by surface waves As a...

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