steady state drainage
DESCRIPTION
Steady State Drainage. Department of Agricultural and Biological Engineering. University of Illinois at Urbana-Champaign. Darcy’s Law. h 1. L. h 2. q: [L/T]. K: [L/T]. L, h: [L]. Bubbling tube. Water inlet tubes. Water. Air. Storage tube. Bubbles. Air at. atmospheric. pressure. - PowerPoint PPT PresentationTRANSCRIPT
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Steady State Steady State DrainageDrainage
Department of Agricultural and Biological
Engineering University of Illinois at Urbana-Champaign
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L)h - h( K = q 21
Lh1
h2
Darcy’s LawDarcy’s Law
q: [L/T] K: [L/T] L, h: [L]
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Bubbling tube
Water inlet tubes
Outlet tube
Outlet holes
Storage tube
Air seal plugSoil
Water
AirBubbles
Water level fixedby bubbling tube
Air at atmosphericpressure
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Inner Cylinder
Outer Cylinder
Mariotte Bottle
Bubbling Tube
Soil
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H1
H2
H3
Hn
Hn+1
K1
K2
Kn
D1
D2
Dn
q
EQUIVALENT K FOR VERTICAL FLOWEQUIVALENT K FOR VERTICAL FLOWWhen flow is
perpendicular to a series of soil layers, the flux through each layer is the
same.
D = D1 + D2 +...+Dn
n
n
2
2
1
1e
KD
KD
KD
D K
...
D)H - H( K = q 1n1
e
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9 ft4 ft K = 2 ft/d
2 ft K = 4 ft/d
3 ft K = 3 ft/d
Ke?
ft/d 2.573.59
42
24
33
9 K e
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Q2
Hb
K1
K2
Kn
D1
D2
Dn
EQUIVALENT K FOR HORIZONTAL FLOWEQUIVALENT K FOR HORIZONTAL FLOW
When flow is parallel to a series of soil layers, the discharge through unit thickness of the system is the
sum of the discharges through the
layers..
n21
nn2211L DDD
KDKDKD K
...
...L
)H - H( K = q baL
Ha
Q1
Qn
L
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IMPERMEABLE LAYER
h
m
d S
2r
Hooghoudt EquationHooghoudt Equation
2e
S)2d4Km(m
q
de
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Hooghoudt EquationHooghoudt Equation
2e
S)2d4Km(m
q
1,3,5,....n S4n
S4n
01n0
e
)e(1n
e48)
rπS
(ln8
Sπ
)S
dnπ2coth(ln16)
rπS
(ln8
Sπd
πd
πd
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Estimating Spacing Estimating Spacing using using The Hooghoudt The Hooghoudt EquationEquation
2e
S)2d4Km(m
q
i)2d4Km(m
S e2
i = Drainage Coefficient
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0.4 1.2
S
6.0
Soil surface
Impervious layer
Water table
For drainage design the following information is available:
depth of tile = 1.2 m; depth to water table = 0.8 m; depth to impermeable layer = 7.2 m; drainage
coefficient = 0.007 m; hydraulic conductivity = 0.8 m/day. Estimate the required drain spacing
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0.4 1.2
S
6.0
Soil surface
Impervious layer
Water table
For drainage design the following information is available:
depth of tile = 4 ft; depth to water table = 1 ft; depth to impermeable layer = 12 ft; drainage coefficient = 3/8 inches; hydraulic conductivity = 2 inch/hr. Estimate the
required drain spacing
3 4
8
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IMPERMEABLE LAYER
h
b
d S
2r
t
Kirkham EquationKirkham Equation
gSr)bK(t4
q
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)2/)2(cos()2/cosh(
)2/)2(cos()2/cosh(ln
)2/cos()2/cosh(
)2/cos()2/cosh(ln2
)4/tan(
)4/)2(tan(ln2
1 hrdhmS
hrdhmS
hrhmS
hrhmS
hd
hrd
m
g
gSr)bK(t4
q
Kirkham EquationKirkham Equation