1Theory of Groundwater FlowTheory of Groundwater FlowTopics1.
Differential Equations of Groundwater Flow2. Boundary conditions3.
Initial Conditions for groundwater prole!s". Flow#et analysis$.
%at&e!atical analysis of so!e si!ple flow
prole!s25.1.Differential Equations5.1.Differential
EquationsExamples of useful use of flow equations in solving Hydro
ro!lems"1# $% drop around a well after 1& years of pumping"'#
(ontaminant )on)entration )hanges after 5 years of remediation
")leanup#"*# (hange in storage of aquifer after use of 5&
years3+athemati)al approa)h +athemati)al approa)h ,-epresent the
G-./0D$1TE- pro)ess !y an equation,2olving the equation,-esult is
hydrauli) head "spa)e3 time#4How is it done4How is it done41n
illustrative example51n illustrative example5'ilty
'and'and'&ale(.( geological prole!5How is it done4How is it
done41n illustrative example51n illustrative example5K = 1K =
10B.Conceptuali)ed !at&e!atical prole!Water Table: variable
head boundaryTop of shale = base of aquifer = NO-Flow boundaryide
No-flow boundaryide No-flow boundary6How is it done4How is it
done41n illustrative example51n illustrative example5K = 1K = 10C.
Calculating t&e &ydraulic &ead distriution*go+erning
equations,h= 908886848280 7876K = 1K = 107Deriving Groundwater
Deriving Groundwater flow Equationsflow EquationsDar)y6s
%awprin)iple of mass )onservationG- Flow equations8.epresentati+e
Ele!entary /olu!e *.E/,%ass inflow rate0 !ass outflow rate1
c&ange in storage wit& ti!e ! y "Deriving Groundwater
Deriving Groundwater flow Equationsflow Equations9The main equation
of The main equation of groundwater flowgroundwater flow,T&is
is a linear paraolic partial differential equation,It2s t&e
!ain equation of groundwater flow in saturated !edia,It is sol+ale
only y nu!erical !et&ods,t&e solution of w&ic&
yields h #!$y$"$t, in a &eterogeneous3 anisotropic confined
aquifer.,(lso 4nown as t&e %iffusion &quation++= x Khx y
Khy z KhzShtx y z s( ) ( ) ( )102implifi)ations of the
equation2implifi)ations of the equation"1# for homogeneous !ut
anisotropi) aquifer5"'# for homogeneous and isotropi)"*# for
hori7ontal flow"8# steady state flow KhxKhyKhzShtx y z s++=222222+
+ =222222hxhyhzSKhts+ =2222hxhySTht+ + =2222220hxhyhz11%apla)e
equation%apla)e equation,one of the most useful field equations
employed in hydrogeology.The solution to this equation des)ri!es
the value of the hydrauli) head at any point in a *9dimensional
flow field,Note: the mapped potentiometric surface represents
"solution" to Laplace's equation for 2dimensional flo! field + +
=2222220hxhyhz125.' :oundary )onditions5.' :oundary )onditions*
types51. Diri)hlet :oundary (ondition"pecified head at a #oundar$'.
0eumann :oundary (ondition"pecified !ater flu% at a #oundar$&'
(auch$ #oundar$ condition)elates h$draulic head to !ater flu%135.*
;nitial (onditions5.* ;nitial (onditions,For steady state
equations.nly !oundary )onditions are needed,For transient
equations5:oundary and initial )onditions are needed,'nitial
(ondition5rovides hydrauli) head everywhere within the domain of
interest !efore simulation !egins0( , , , 0) ( , , ) h x y z h x y
z =145.8 Flownet 1nalysis5.8 Flownet 1nalysis151617Flownets3
general features in a 20D flow do!ain Flownets3 general features in
a 20D flow do!ain ,1. 2treamlines are perpendi)ular to
equipotential lines. ;f the hydrauli)9head drops !etween the equip.
lines are the same3 the streamlines and equip. lines form
)urvilinear squares. ,'. The same quantity of ground water flows
!etween ad
