Drainage of Agricultural Lands - Practices of Irrigation and On-farm Water Management - page 353

Limitations of Hooghoudt Equation

The Hooghoudt's equation assumes an elliptical water table, which occurs below the
soil surface. Sometimes excess precipitation may raise the water table to the soil sur-
face, and ponded water remains on the surface for relatively long periods. For such
conditions, the application of Hooghoudt's equation based on the D-F assumptions
has limitations to calculate the subsurface drainage flux into the tile drains. In case
of surface ponding, the D-F assumptions will not hold and the streamlines will be
concentrated near the drains with most of water entering the soil surface in that
vicinity (Kirkham, 1957 ) .

Estimation of Equivalent Depth

The equivalent depth can be obtained as (Hooghoudt, 1940 )

S
8ln S
π

π

d e = (9.18)

r 0

where r 0 is the radius of drain.
Moody (1966) proposed the following approximation for d e :

D D

S ≤

d e =

3.4] , 0

< 0.3

1 + ( D / S )[(8 /π )ln( D / r 0 ) −

(9.19)

S D

S >

=

1.15] ,

0.3

(8 /π )[ln( S / r 0 ) −

Closed-Form Solution for Equivalent Depth

Van der Molen and Wesseling ( 1991 ) developed closed-form expression for the
equivalent depth ( d e ) that can replace the Hooghoudt's tables:

ln

F ( x ) d e = π

S
8

S
π r +

(9.20)

where

2 π D

x =

S

and

4e − 2 nx
n (1

F ( x ) =

e − 2 nx ) , with n = 1,3,5

...

−

The F ( x ) converges rapidly for x >0.5.
The above equation must be solved iteratively, as both “ d e ” and “ S ” are unknown.