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Darcys Law
Darcys law provides an accuratedescription of the flow of
groundwater in almost all hydrogeologicenvironments.
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Darcys Law
Henri Darcy established empirically that the
flux of water through a permeable formationis proportional to
the distance between top
and bottom of the soil column. The constant
of proportionality is called the hydraulic
conductivity(K.
! " #$%& v 'h& and v )$*
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Hydraulic Conductivity
K represents a measure of the ability forow through porous
media:
K is highest for gravels - !" to " cm#sec K is high for sands -
"-$to "-%cm#sec
K is moderate for silts - "-& to "-'cm#sec
K is lowest for clays - "-(to "-)cm#sec
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Darcys Experimental
Setup:Head loss h1- h2 determines flow rate
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Darcys Law Therefore&
V = K (h/L)
and since
Q= VA Q= KA(dh/dL)
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Conditions +n ,eneral& Darcys *aw holds
for- ). aturated flow and unsaturatedflow /. teady0state and
transient flow 1.2low in a3uifers and a3uitards 4. 2low in
homogeneous and heteogeneous systems
5. 2low in isotropic or anisotropic media6.2low in roc7s and
granular media
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Darcy elocity Vis the specific discharge (Darcy velocity.
(' indicates that Voccurs in the direction of
the decreasing head.
pecific discharge has units of velocity.
The specific discharge is a macroscopicconcept& and is
easily measured. +t should be
noted that Darcys velocity is different 8.
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Darcy ! Seepa"e elocity
Darcy velocity is a fictitious velocity
since it assumes that flow occurs
across the entire cross0section of
the soil sample. 2low actually ta7es
place only through interconnected
pore channels.
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Darcy ! Seepa"e elocity
2rom the 9ontinuity :3n-
Q =A vD= AVVs
' ;here-
Q" flow rate
A" cross0sectional area of
materialAV" area of voids
Vs" seepage velocity
vD" Darcy velocity
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E#uations o$
%round &ater 'low
Description of ground water flow is based
on:1. Darcys Law
2. Continuity Equation describes
conser!ation of fluid "assduring flow t#roug# a porous
"ediu"$ results in a partial
differential equation of flow.
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Example o$ Darcys Law
% confined aquifer #as a source of rec#arge.
& for t#e aquifer is '( ")day* and n is (.2.
+#e pie,o"etric #ead in two wells 1((( " apart
is '' " and '( " respecti!ely* fro" a co""on
datu".
+#e a!erage t#ic-ness of t#e aquifer is ( "*
and t#e a!erage widt# is ' -".
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Calculate:
a/ t#e rate of flow t#roug# t#e aquifer
0b/ t#e ti"e of tra!el fro" t#e #ead of t#e
aquifer to a point -" downstrea" *assume no dispersion or
diffusion
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(he solution
9ross0ectional area"1>(5()>>> " )5 x )>4 m/
Hydraulic gradient "(5505>$)>>> " 5 x )>01
?ate of 2low for K " 5> m$day# " (5> m$day (@5 x
)>)
m/ " 1@&5>> m1$day
Darcy !elocity-
! " #$% " (1@&5>>m1$day $ ()5x )>4 m/ "
>./5m$day
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Limitations o$ the
Darcian )pproach). 2or ?eynolds Bumber& ?e& C )>
where the flow is
turbulent& as in the immediate vicinity of pumped
wells.
/. ;here water flows through extremely fine0grained
materials (colloidal clay
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Confned Aquier
Confining Layer
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Example *
9onsider a )0ft length of river (and channel.
Q = KA %(h& h') / L
;here-
A" (1> x ) " 1> ft/ K
" (>./5 ft$hr (/4 hr$day " 6 ft$day
Therefore&
# " E6 (1> ()/> ' ))>F $ />>>
" >.G ft1$day$ft length " >.G ft/$day
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Permeameters
Constant Head Falling Head
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Darcys Law
Darcys Law can be used to compute flow rate in almost
any aquifer system where heads and areas are knownfrom
wells.
