Darcy’s Law
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Transcript of Darcy’s Law
Darcy’s Law
1. Vol. = K.I.A.T2. Q= K.I.A3. V=K.I4. Q = T.I.W
Assumption: Steady state flow condition
Theis, 1935, New MexicoDeveloped the transient GW flow equation
GW Flow Equation in radial form
t
h
T
S
r
h
r
h
r
2
2
.1
r = distance from a wellh= hydraulic head at distance rS = storage coefficient of aquiferT = Transmissivityt = elapsed time
Groundwater Flow
1.Steady State
2.Non-Steady (Transient flow)
GW Flow Toward a WellIn Radial Coordinates
t
h
T
S
z
h
y
h
x
h
2
2
2
2
2
2
GW flow equation in Cartesian Coordinated
X, y and z are distance from origin
Theis (1935) used the concept ofHeat sink/source to solve theRadial form of GW flow equation
duu
e
T
Qs
u
u
4
s = drawdownQ =pumping rateT = transmissivity
tT
Sru
.4
2
duu
euW
u
u
)(
W(u) =[-0.5772-lnu+u-u2/(2.2!)+u3/(3.3!)-u4/(4.4!)+u5/(5.5!)-…]
Normally five elements within the bracketIs sufficient.
You can also use table 4.1, p29
Theis assumptions:1. No external recharge or discharge2. The aquifer is homogeneous, Isotropic andHas uniform thickness3. Aquifer is confined4.The well penetrates the entire aquifer and Is screened all the way through aquifer5. The flow lines are horizontal6.The well diameter is infinitely small7.The head in the aquifer responds instantly8. The aquifer is infinite
Why do we need Theis eq.
What is the first thing we need to doIf we want to drill a well?
1.Preliminary investigation using existing data2. Get a permit for a test holeNeed to advertise the intent.You get sued for infringement
If infringement is proven,What are possible remedies?
1. Rejection of permit2. Financial compensation for the impact3. Night versus day pumping4. Gun?
Cooper-Jacob eq.
01.04
]ln5772.0[42
Tt
Sru
uT
Qs
01.04
]ln56.0[ln42
Tt
Sru
uT
Qs
01.04
]4
ln56.0[ln42
2
Tt
Sru
Tt
Sr
T
Qs
01.04
])4(56.0
[ln42
2
Tt
Sru
Sr
Tt
T
Qs
]25.2
[ln4 2Sr
Tt
T
Qs
If s, drawdown = 0
2.25Tt/r2S =1
2
2
2
25.2
183.0
)(log
25.2log
183.0log
183.0
25.2log
183.0
r
TtS
s
QT
sa
btasSr
Tt
T
Qt
T
Qs
Sr
Tt
T
Qs
2
3.0
264
r
TtS
s
QT
In U.S. conventional unitst, is dayT is gpd/ftr is in ft