Steady State Drainage

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