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8-Flow_In_Aquifers
Course: CE 374, Spring 2002School: University College of...
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Kx qx 2/7/09 1 2/7/09 h =S t x qx = K K h x x h h =S x t x h h h h + Ky + Kz =S x y z y z t Ground surface Head in confined aquifer Confining Layer Bedrock Qx Confined aquiferb K h 1b h(x,y,t)= h(x,y,z,t)dz b0 1b q x (x,y,t)= q x (x,y,z,t)dz b0 Q x = bq x 2 2/7/09 Hydraulic gradient = 1 m/m ce rfa Su ric et iom nt te d Po Be ing fin on C Transmissivity, T, volume of water flowing...
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Kx
qx 2/7/09
1
2/7/09
h =S t x
qx = K
K
h x
x
h h =S x t
x
h h h h + Ky + Kz =S x y z y z t
Ground surface Head in confined aquifer Confining Layer
Bedrock
Qx
Confined aquiferb K
h
1b h(x,y,t)= h(x,y,z,t)dz b0
1b q x (x,y,t)= q x (x,y,z,t)dz b0
Q x = bq x
2
2/7/09
Hydraulic gradient = 1 m/m
ce rfa Su ric et iom nt te d Po Be ing fin on C
Transmissivity, T, volume of water flowing an area 1 m x b under hydraulic gradient of 1 m/m
1m
b
1m 1m
T =K b
1b b0
er uif Aq ed fin on C
K(x,y)=
K(x,y,z)dz
Conductivity, K, volume of water flowing an area 1 m x 1 m under hydraulic gradient of 1 m/m
Qx h =S x t
Ground surface Head in confined aquifer Confining Layer
Q x = Tx h x
Bedrock
Qx
Confined aquiferb K
h
h h Tx =S x x t 1 h Sh r = rr r Tt
Radial Coordinates
3
2/7/09
x Tx d 2h x2 h h =0 =S x t
Ground surface
T
=0
steady flow
h(x)
Confining Layer
hA
Confined aquifer Qx K Bedrock L b hB
hA h h(x) = h A + B x L
Head in the aquifer
h hA h(x) = h A + B x = 100 0.02x m L
Ground surface
q= K
hB h A L 80 100 1000
= (20 m /d) = 0.4 m /day
Confining Layer
v=
hA Confined aquifer Qx K Bedrock L b hB
q
= 1.14 m /day
4
2/7/09
h )h x
Qx = qx h = ( K h Qx = Sy x t
x
Kh
h h = Sy t x
5
2/7/09
Ground Surface Water Table
x
Kh
h h = Sy t x
hA h hB Flow
dh d Kh =0 dx
dx d 2 h2 dx 2
Bedrock
x
L
2 h 2 (x) = h A + (
( )=0
2 2 hB h A )x L
Q=( K
2 2 dh K dh 2 K hB h A )h = = dx 2 dx 2 L
Ground Surface Water Table
hA h
Flow hB
Bedrock
x
L
Q=
2 2 2 2 K hB h A 86.4 m /d 6.5 4 = = 7.56 m 3 /d / m 2 L 150 2
6
2/7/09
N, Infiltration
x
Kh
h h + N = Sy t x
Constant K
Ground Surface Water Table
Steady Flow
h
hMax Flow hB
d 2 h2 dx
2
( )=
hA
2
N K
Bedrock
x
L
2 h 2 (x) = h A +
2 N h 2 hA L+ B x K L
N2 x K
N, Infiltration
Q(x) =
K d(h 2 ) 2 dx
hL
Ground Surface Water Table
h
hMax Flow hR
2 dh 2 N h 2 hA = L+ B K dx L
N 2x K
Bedrock
x
L
Q(x) =
NL h2 h2 K R L + Nx 2 2L
x divide =
L K 2 2 + (hR hL ) 2 2NL
7
2/7/09
N, Infiltration
Ground Surface Water Table
h hL
hMax Flow hR
Bedrock
x
L
Q(0) =
20 1.37 ...
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