Contents preface (VII) introduction 1—37

Fig. 5.25. Mole drain
Beam
Traction
	Blade
Mole	Expander	Mole channel

Fig. 5.26 Mole plough
Consider two drains at a spacing of B and the resulting drained water table as shown in Fig. 5.27. An impermeable layer underlies the drain at a depth d. Rainfall intensity (or rate of application of irrigation water) is uniform and is equal to r_a (m/s). Hooghoudt made the following assumptions to obtain a solution of the problem (19):
(i) The soil is homogeneous and isotropic,
(ii) The hydraulic gradient at any point is equal to the slope of the water table above the point, i.e., dh/dx, and
(iii) Darcy’s law is valid.
Using Darcy’s law one can write,

	q = ky ^dy	(5.25)
	x	dx
	P (x,y)		P (x,y)
	H		h
	h
	B/2		B
y	d		d
	x
	(a) Deep open drains		(b) Sub-surface drains

Fig. 5.27 Line sketch of drains

222 IRRIGATION AND WATER RESOURCES ENGINEERING

in which qx is the discharge per unit length of drain at a section x distance away from the

drain, and k is the coefficient of permeability of the soil. Also,

q = ^F

B

− x ^I

r

(5.26)

x

G

2

J

a

H

K

Using Eqs. (5.25) and (5.26), one can write

F

B

− x^I

r

= ky

dy

G

J

a

dx

H 2

K

∴

B

r

dx − r

xdx = ky dy

On integrating,

2 a

a

ra

B

x − ra

x^2

= k

y^2

+ C

2

2

2

The constant of integration C can be determined by using the boundary condition: at x = 0, y = h + d

∴

C =

−

k(h + d)^2

2

^ra

B

x − ra

x^2

=

k

[ y^2 − (h + d)^2 ]

2

2

2

Further, at x = B/2, y = H + d

ra

B^2

− ra

B^2

=

k

[(H + d)^2 − (h + d)^2 ]

4

8

2

or

ra

B^2

= k [(H + d)^2 – (h + d)^2]

4

∴

B^2 = ^4r

^k [(H + d)^2 – (h + d)^2]

(5.27)

a

Equation (5.27) is Hooghoudt’s equation for either open ditch drains or subsurface drains. If q_d is the discharge per unit length of drain that enters the drain from two sides of the drain, then

	qd = ra B
∴	q =	4k		[(H + d)^2 − (h + d)^2 ]	(5.28)
B
		d
	In practice, the drain is considered empty (i.e., h = 0). Equation (5.28) then reduces to
		q =	4k	[ H + d) ^2 − ( d) ^2 ]		(5.29)
				B
	d
or	q = ^4^kH (H + 2d)
	d	B
i.e.,	B^2 =	4kH	(H + 2d)	(5.30)
r
		a

Thus, knowing q_d, one can determine the spacing B of the drains. The design drain discharge (or the drainage coefficient which is defined as the amount of water that must be

CANAL IRRIGATION

223

removed in a 24-hour period) primarily depends on the rainfall rate, size of the watershed, and the amount of surface drainage water that is admitted to the drainage system and is usually taken as equal to one per cent of average rainfall in one day. Thus,

qd = ^{0.01 × ra × B} m³/s per metre length of drain.

24 × 3600

Here, r_a is the average rainfall intensity in metres, and B is the spacing of the drains in metres. The value of B is generally between 15 and 45 m. The main drawback of the gravity drainage system is that it is not capable of lowering the water table to large depths.
Drainage wells offer a very effective method of draining an irrigated land. The soil permeability and economic considerations decide the feasibility of well drainage. Drainage wells pump water from wells drilled or already existing in the area to be drained. Design of a drainage well system will be based on established principles of well hydraulics which have been discussed in Chapter 4.
The above-mentioned remedial methods can be grouped as structual measures. In addition, the following non-structual measures can also be resorted to for preventing or reducing the menace of waterlogging:

1. 
   Adoption of tolerant crops
   

2. 
   Restricting canal supplies close to crop-water needs
   

3. 
   Switch over to drip irrigation
   

4. 
   Conjunctive use of surface and ground water
   

5. 
   Rationalization of water and power pricing policies
   

6. 
   Improvement in canal irrigation management
   

7. 
   Incentives for reclamation of land
   

In arid regions, the bio-drainage (plantation of trees having high transpiration rates) would help in controlling the rise of ground water table and soil salinity. In addition, the bio-mass so grown acts as shelter belt in light soil area against shifting sands and dunes such as in Indira Gandhi Nahar Pariyojna (IGNP) command area in which eucalyptus trees and other trees of similar species were planted. The plantation was very effective in lowering of water table (20).