Groundwater and Seepage

Groundwater and Seepage - 18 Groundwater and Seepage 18.1...

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© 2003 by CRC Press LLC 18 Groundwater and Seepage 18.1 Introduction 18.2 Some Fundamentals Bernoulli’s Equation • Darcy’s Law • Reynolds Number • Homogeneity and Isotropy • Streamlines and Equipotential Lines 18.3 The Flow Net 18.4 Method of Fragments 18.5 Flow in Layered Systems 18.6 Piping 18.1 Introduction Figure 18.1 shows the pore space available for flow in two highly idealized soil models: regular cubic and rhombohedral . It is seen that even for these special cases, the pore space is not regular, but consists of cavernous cells interconnected by narrower channels. Pore spaces in real soils can range in size from molecular interstices to cathedral-like caverns. They can be spherical (as in concrete) or flat (as in clays), or display irregular patterns which defy description. Add to this the fact that pores may be isolated (inaccessible) or interconnected (accessible from both ends) or may be dead-ended (accessible through one end only). In spite of the apparent irregularities and complexities of the available pores, there is hardly an industrial or scientific endeavor that does not concern itself with the passage of matter, solid, liquid, or gaseous, into, out of, or through porous media. Contributions to the literature can be found among such diverse fields (to name only a few) as soil mechanics, groundwater hydrology, petroleum, chemical, and metallurgical engineering, water purification, materials of construction (ceramics, concrete, timber, paper), chemical industry (absorbents, varieties of contact catalysts, and filters), pharmaceutical industry, traffic flow, and agriculture. The flow of groundwater is taken to be governed by Darcy’s law, which states that the velocity of the flow is proportional to the hydraulic gradient . A similar statement in an electrical system is Ohm s law and in a thermal system, Fourier’s law . The grandfather of all such relations is Newton’s laws of motion . Table 18.1 presents some other points of similarity. 18.2 Some Fundamentals The literature is replete with derivations and analytical excursions of the basic equations of steady state groundwater flow [e.g., Polubarinova-Kochina, 1962; Harr, 1962; Cedergren, 1967; Bear, 1972; Domenico and Schwartz, 1990]. A summary and brief discussion of these will be presented below for the sake of completeness. Milton E. Harr Purdue University
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Bernoulli’s Equation Underlying the analytical approach to groundwater flow is the representation of the actual physical system by a tractable mathematical model. In spite of their inherent shortcomings, many such analytical models have demonstrated considerable success in simulating the action of their prototypes. As is well known from fluid mechanics, for steady flow of nonviscous incompressible fluids, Bernoulli’s equation [Lamb, 1945] (18.1) FIGURE 18.1 Idealized void space.
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Groundwater and Seepage - 18 Groundwater and Seepage 18.1...

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