© 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 cathedrallike 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
deadended
(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., PolubarinovaKochina, 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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View Full DocumentBernoulli’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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 Thorton
 Fluid Dynamics, CRC Press LLC, flow nets

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