Drainage of Agricultural Lands - Practices of Irrigation and On-farm Water Management - page 355

9.5.2 Formula for Irregular Drain System

Most investigations, both theoretical and experimental, have focused on parallel
drainage systems with equally spaced tiles. However, in many watersheds (e.g., as
those in Illinois), parallel systems do not occur as frequently as irregular systems.
Irregular tile systems predominate in areas where the majority of the tiles drain
small depressional areas, and thus tile lines are placed at irregular angles and spac-
ings. In these systems, a constant spacing parameter does not exist or cannot be
easily defined.
Irregular and parallel tile systems are hydraulically different, as a single tile
draws water from a semi-infinite distance on either side (Fig. 9.14 ) , while the region
of influence of each tile in a parallel system is constrained by the neighboring
tiles.

Fig. 9.14 Schematic of flow
to single drain

2r 0

h L

h 0

L

Cook et al. ( 2001 ) derived equation for random and irregular tile drainage system.
Their equation is

K
L ( h L −

h 0 ) q 0 = (9.23)

where

the flow rate at the tile drain from each side (m 3 /s) q 0 =

hydraulic conductivity (m 3 /m 2 /s)

=

K

L = the distance at which the water table becomes essentially horizontal (m)

h L = height of water table above the impervious layer at distance L (m)

h 0 = height of drain above the impermeable layer (m)

The total drain outflow would be twice q 0 , since water flows into the drain from
both sides. It should be noted that this is identical to the result for parallel systems
if L is replaced by the half spacing, S/ 2.