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
Steady State Steady State DrainageDrainage
Department of Agricultural and Biological
Engineering University of Illinois at Urbana-Champaign
L)h - h( K = q 21
Lh1
h2
Darcy’s LawDarcy’s Law
q: [L/T] K: [L/T] L, h: [L]
Bubbling tube
Water inlet tubes
Outlet tube
Outlet holes
Storage tube
Air seal plugSoil
Water
AirBubbles
Water level fixedby bubbling tube
Air at atmosphericpressure
Inner Cylinder
Outer Cylinder
Mariotte Bottle
Bubbling Tube
Soil
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
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
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
IMPERMEABLE LAYER
h
m
d S
2r
Hooghoudt EquationHooghoudt Equation
2e
S)2d4Km(m
q
de
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
Estimating Spacing Estimating Spacing using using The Hooghoudt The Hooghoudt EquationEquation
2e
S)2d4Km(m
q
i)2d4Km(m
S e2
i = Drainage Coefficient
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
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
IMPERMEABLE LAYER
h
b
d S
2r
t
Kirkham EquationKirkham Equation
gSr)bK(t4
q
)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