Drainage of Agricultural Lands - Practices of Irrigation and On-farm Water Management - page 351

Putting the values, discharge capacity for the tertiary drain,

40,000 m 3 /s Q t =

× ×

0.6 9.72222E-06

0.233 m 3 /s

=

3=0.7m 3 /s

Discharge capacity for the secondary drain, Q s = Q t × 3 = 0.233 ×

4=2.8m 3 /s(Ans.) Discharge capacity for the main drain, Q m = Q s × 4=0.7 ×

9.5 Equations/Models for Subsurface Drainage Design

9.5.1 Steady-State Formula for Parallel Drain Spacing

9.5.1.1 Hooghoudt's Equation

Definition Sketch

Hooghoudt's equation is widely used in subsurface drainage design. It can also be
used for sloping land and to account for entrance resistance encountered by the
water upon entering the drains. Hooghoudt's equation for drain spacing (Hooghoudt,
1940 ) can be described as

4 k a h 2
q

8 k b d e h
q

S 2

= + (9.15)

where

S = drain spacing (L)

q drainage coefficient (L/T)

k a =

=

hydraulic conductivity of layer above the drain (L/T)

k b = hydraulic conductivity of layer below the drain (L/T)

=

h height of water at the midway between drains under stabilized condition (L)

d e = equivalent depth (L)

The first term of the equation gives the spacing for the flow above the plane of
the bottom of the drain, while the second term gives the spacing for the flow below
the plane. The definition sketch of elements of Hooghoudt's drain spacing equation
is given in Fig. 9.13
Here, “ D ” is the actual depth of impervious layer from the drain, and “ d e ”is
the equivalent depth of “ D ” to correct the resistance due to radial flow, which was
assumed as horizontal flow. “Equivalent depth” represents the imaginary thinner
soil layer through which the same amount of water will flow per unit time as in
the actual situation. The resulting higher flow per unit area introduces an extra head
loss, which accounts for (and thus resembles to) the head loss caused by converging
flow lines.